U.S. patent application number 17/745608 was filed with the patent office on 2022-09-01 for methods, systems and apparatus for calibrating data using relaxed benchmark constraints.
The applicant listed for this patent is The Nielsen Company (US), LLC. Invention is credited to Ludo Daemen, Christophe Koell, Alexander Radev, Vippal Savani, Robert C. Smith, William Somers, Edmond Wong.
Application Number | 20220277244 17/745608 |
Document ID | / |
Family ID | 1000006335332 |
Filed Date | 2022-09-01 |
United States Patent
Application |
20220277244 |
Kind Code |
A1 |
Daemen; Ludo ; et
al. |
September 1, 2022 |
METHODS, SYSTEMS AND APPARATUS FOR CALIBRATING DATA USING RELAXED
BENCHMARK CONSTRAINTS
Abstract
Methods, systems, and apparatus for calibrating data using
relaxed benchmarks constraints are described. An example apparatus
for generating a unique solution when calibrating data via a
calibration model having relaxed benchmark constraints includes
processor circuitry to execute computer-readable instructions. The
computer-readable instructions are to execute the calibration model
based on matrix data, a target loss function, a weight loss
function, and a budget parameter. The computer-readable
instructions are to determine calibrated weights resulting from
execution of the calibration model. The computer-readable
instructions are to incorporate a stability parameter into the
calibration model in response to determining that the calibrated
weights do not provide a unique solution for the executed
calibration model. The stability parameter is to reduce an
influence of the budget parameter on the calibration model to
enable the generation of a unique solution.
Inventors: |
Daemen; Ludo; (Duffel,
BE) ; Smith; Robert C.; (New York, NY) ; Wong;
Edmond; (New York, NY) ; Radev; Alexander;
(New York, NY) ; Savani; Vippal; (Oxfordshire,
GB) ; Koell; Christophe; (Brussels, BE) ;
Somers; William; (New York, NY) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
The Nielsen Company (US), LLC |
New York |
NY |
US |
|
|
Family ID: |
1000006335332 |
Appl. No.: |
17/745608 |
Filed: |
May 16, 2022 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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16942429 |
Jul 29, 2020 |
11361264 |
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17745608 |
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15583337 |
May 1, 2017 |
10776728 |
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16942429 |
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62346897 |
Jun 7, 2016 |
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62378041 |
Aug 22, 2016 |
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62379205 |
Aug 24, 2016 |
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62379517 |
Aug 25, 2016 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G06Q 10/06313 20130101;
G06F 17/16 20130101 |
International
Class: |
G06Q 10/06 20060101
G06Q010/06; G06F 17/16 20060101 G06F017/16 |
Claims
1. An apparatus for generating a unique solution when calibrating
data via a calibration model having relaxed benchmark constraints,
the apparatus comprising: at least one memory; computer-readable
instructions; and processor circuitry to execute the
computer-readable instructions to: execute the calibration model
based on matrix data, a target loss function, a weight loss
function, and a budget parameter, the matrix data based on
criteria-based input data to be incorporated into the target loss
function and unit-based input data to be incorporated into the
weight loss function; determine calibrated weights resulting from
execution of the calibration model; and incorporate a stability
parameter into the calibration model in response to determining
that the calibrated weights do not provide a unique solution for
the executed calibration model, the stability parameter to reduce
an influence of the budget parameter on the calibration model to
enable the generation of a unique solution.
2. The apparatus as defined in claim 1, wherein the stability
parameter is to prevent a minimization procedure of the calibration
model from reaching a flat region of the target loss function.
3. The apparatus as defined in claim 1, wherein the matrix data is
based on panelist data for a group of participants having one or
more associated demographic representations, the criteria-based
input data defined based on the one or more demographic
representations.
4. The apparatus as defined in claim 1, wherein the budget
parameter is an upper constraint that a weight loss value
determined via the weight loss function is allowed to obtain.
5. The apparatus as defined in claim 1, wherein the processor
circuitry is to: re-execute the calibration model based on the
matrix data, the target loss function, the weight loss function,
the budget parameter, and the stability parameter; and re-determine
the calibrated weights resulting from the re-execution of the
calibration model, the re-determined calibrated weights to provide
a unique solution for the re-executed calibration model.
6. The apparatus as defined in claim 1, wherein the criteria-based
input data includes (a) criteria variables and (b) at least one of
targets for the criteria variables, upper and lower bounds for the
criteria variables, scaling parameters for the criteria variables,
or importance parameters for the criteria variables.
7. The apparatus as defined in claim 1, wherein the unit-based
input data includes (a) unit variables and (b) at least one of
initial weights for the unit variables, upper and lower bounds for
the unit variables, or size parameters for the unit variables.
8. A tangible machine-readable storage medium comprising
instructions that, when executed, cause a processor to at least:
execute a calibration model based on matrix data, a target loss
function, a weight loss function, and a budget parameter, the
calibration model having relaxed benchmark constraints, the matrix
data based on criteria-based input data to be incorporated into the
target loss function and unit-based input data to be incorporated
into the weight loss function; determine calibrated weights
resulting from the execution of the calibration model; and
incorporate a stability parameter into the calibration model in
response to determining that the calibrated weights do not provide
a unique solution for the executed calibration model, the stability
parameter to reduce an influence of the budget parameter on the
calibration model to enable the generation of a unique
solution.
9. The tangible machine-readable storage medium as defined in claim
8, wherein the stability parameter is to prevent a minimization
procedure of the calibration model from reaching a flat region of
the target loss function.
10. The tangible machine-readable storage medium as defined in
claim 8, wherein the matrix data is based on panelist data for a
group of participants having one or more associated demographic
representations, the criteria-based input data defined based on the
one or more demographic representations.
11. The tangible machine-readable storage medium as defined in
claim 8, wherein the budget parameter is an upper constraint that a
weight loss value determined via the weight loss function is
allowed to obtain.
12. The tangible machine-readable storage medium as defined in
claim 8, wherein the instructions, when executed, are further to
cause the processor to: re-execute the calibration model based on
the matrix data, the target loss function, the weight loss
function, the budget parameter, and the stability parameter; and
re-determine the calibrated weights resulting from the re-execution
of the calibration model, the re-determined calibrated weights to
provide a unique solution for the re-executed calibration
model.
13. The tangible machine-readable storage medium as defined in
claim 8, wherein the criteria-based input data includes (a)
criteria variables and (b) at least one of targets for the criteria
variables, upper and lower bounds for the criteria variables,
scaling parameters for the criteria variables, or importance
parameters for the criteria variables.
14. The tangible machine-readable storage medium as defined in
claim 8, wherein the unit-based input data includes (a) unit
variables and (b) at least one of initial weights for the unit
variables, upper and lower bounds for the unit variables, or size
parameters for the unit variables.
15. A method for generating a unique solution when calibrating data
via a calibration model having relaxed benchmark constraints, the
method comprising: executing, by executing one or more computer
readable instructions with a processor, the calibration model based
on matrix data, a target loss function, a weight loss function, and
a budget parameter, the matrix data based on criteria-based input
data to be incorporated into the target loss function and
unit-based input data to be incorporated into the weight loss
function; determining, by executing one or more computer readable
instructions with the processor, calibrated weights resulting from
the executing of the calibration model; and incorporating, by
executing one or more computer readable instructions with the
processor, a stability parameter into the calibration model in
response to determining that the calibrated weights do not provide
a unique solution for the executed calibration model, the stability
parameter to reduce an influence of the budget parameter on the
calibration model to enable the generation of a unique
solution.
16. The method as defined in claim 15, wherein the stability
parameter is to prevent a minimization procedure of the calibration
model from reaching a flat region of the target loss function.
17. The method as defined in claim 15, wherein the matrix data is
based on panelist data for a group of participants having one or
more associated demographic representations, the criteria-based
input data defined based on the one or more demographic
representations.
18. The method as defined in claim 15, wherein the budget parameter
is an upper constraint that a weight loss value determined via the
weight loss function is allowed to obtain.
19. The method as defined in claim 15, further including:
re-executing the calibration model based on the matrix data, the
target loss function, the weight loss function, the budget
parameter, and the stability parameter; and re-determining the
calibrated weights resulting from the re-executing of the
calibration model, the re-determined calibrated weights to provide
a unique solution for the re-executed calibration model.
20. The method as defined in claim 15, wherein the criteria-based
input data includes (a) criteria variables and (b) at least one of
targets for the criteria variables, upper and lower bounds for the
criteria variables, scaling parameters for the criteria variables,
or importance parameters for the criteria variables, and wherein
the unit-based input data includes (c) unit variables and (d) at
least one of initial weights for the unit variables, upper and
lower bounds for the unit variables, or size parameters for the
unit variables.
Description
RELATED APPLICATIONS
[0001] This application arises from a continuation of U.S. patent
application Ser. No. 16/942,429, filed Jul. 29, 2020, which is a
continuation of U.S. patent application Ser. No. 15/583,337, filed
May 1, 2017, which claims priority to U.S. Provisional Patent
Application Ser. No. 62/346,897, filed Jun. 7, 2016, U.S.
Provisional Patent Application Ser. No. 62/378,041, filed Aug. 22,
2016, U.S. Provisional Patent Application Ser. No. 62/379,205,
filed Aug. 24, 2016, and U.S. Provisional Patent Application Ser.
No. 62/379,517, filed Aug. 25, 2016. The entireties of U.S. patent
application Ser. No. 16/942,429, U.S. patent application Ser. No.
15/583,337, U.S. Provisional Patent Application Ser. No.
62/346,897, U.S. Provisional Patent Application Ser. No.
62/378,041, U.S. Provisional Patent Application Ser. No.
62/379,205, and U.S. Provisional Patent Application Ser. No.
62/379,517 are hereby incorporated by reference herein.
FIELD OF THE DISCLOSURE
[0002] This disclosure relates generally to methods, systems, and
apparatus for calibrating data and, more specifically, to methods,
systems, and apparatus for calibrating data using relaxed benchmark
constraints.
BACKGROUND
[0003] Traditional models and/or techniques for calibrating data
adjust and/or modify projection weights for the purpose of
improving upon the accuracy of estimates that may be yielded from
applying the projection weights to panelist and/or reporting data
(e.g., survey data). The goal of such traditional calibration
models and/or techniques is to adjust and/or modify the projection
weights such that the weighted totals and/or results of the
panelist and/or reporting data closely match known totals and/or
results of reference and/or benchmark data (e.g., census data).
[0004] Traditional calibration models and/or techniques are
executed and/or performed in a "hard" manner, whereby the
projection weights are adjusted and/or modified such that the
estimated totals of the panelist and/or reporting data match
exactly with the known totals of the reference and/or benchmark
data. Such traditional models and/or techniques for calibrating
data are accordingly referred to herein as "hard calibration"
models and/or techniques.
BRIEF DESCRIPTION OF THE DRAWINGS
[0005] FIG. 1 is a block diagram of an example calibration
apparatus constructed in accordance with the teachings of this
disclosure.
[0006] FIG. 2 is a flowchart representative of example machine
readable instructions that may be executed at the example
calibration apparatus of FIG. 1 to calibrate data using relaxed
benchmark constraints incorporated into a soft calibration
model.
[0007] FIG. 3 is a flowchart representative of example machine
readable instructions that may be executed at the example
calibration apparatus of FIG. 1 to determine criteria-based input
data for the target loss function of the soft calibration model to
be executed by the calibration apparatus.
[0008] FIG. 4 is a flowchart representative of example machine
readable instructions that may be executed at the example
calibration apparatus of FIG. 1 to determine unit-based input data
for the weight loss function of the soft calibration model to be
executed by the calibration apparatus.
[0009] FIG. 5 is a flowchart representative of example machine
readable instructions that may be executed at the example
calibration apparatus of FIG. 1 to determine model parameter data
for the soft calibration model to be executed by the calibration
apparatus.
[0010] FIG. 6 is a flowchart representative of example machine
readable instructions that may be executed at the example
calibration apparatus of FIG. 1 to validate the soft calibration
model executed by the calibration apparatus.
[0011] FIG. 7 is an example processor platform capable of executing
the instructions of FIGS. 2-6 to implement the example calibration
apparatus of FIG. 1.
[0012] Certain examples are shown in the above-identified figures
and described in detail below. In describing these examples,
identical reference numbers are used to identify the same or
similar elements. The figures are not necessarily to scale and
certain features and certain views of the figures may be shown
exaggerated in scale or in schematic for clarity and/or
conciseness.
DETAILED DESCRIPTION
[0013] Clients of data measurement companies expect that panelist
and/or reporting data (e.g., data obtained from tightly controlled
participants having a particular demographic representation) should
reasonably match reference and/or benchmark data (e.g., raw data
acquired from the market, such as actual sales dollars from retail
stores that may be obtained from scanner data at checkout). In the
event that a data measurement company's panelist and/or reporting
data is substantially different from the reference and/or benchmark
data, the data measurement company's clients may question the
accuracy and/or validity of the data measurement company's ability
to accurately project sales and/or usage numbers using the panelist
and/or reporting data.
[0014] Data measurement companies often calibrate panelist and/or
reporting data to reference and/or benchmark data utilizing the
traditional hard calibration models and/or techniques described
above. At least one drawback of such hard calibration models and/or
techniques is that the calibration weights may begin to take on a
relatively large magnitude. While some demographic groups of
panelist and/or reporting data might align well with the reference
and/or benchmark data when such large-magnitude calibration weights
are applied, these same calibration weights may result in
substantial errors for other demographic groups.
[0015] In contrast to the traditional hard calibration models
and/or techniques described above, the methods, systems and
apparatus for calibrating data disclosed herein use relaxed
benchmark constraints. As used herein, the term "soft calibration"
refers to a convex optimized calibration model and/or technique
providing a unique solution for calibrating a set of weights (e.g.,
projection weights) relative to a set of relaxed benchmark
constraints. The benchmark constraints that may be implemented in
the disclosed soft calibration models and/or techniques are relaxed
(e.g., loosened, broadened, and/or made less rigid) relative to the
benchmark constraints that might otherwise be implemented in
traditional hard calibration models and/or techniques. For example,
the disclosed soft calibration models and/or techniques relax the
exact matching requirement of the traditional hard calibration
process.
[0016] Unlike hard calibration models and/or techniques requiring
that estimated totals associated with projection weights match
reference and/or benchmark totals precisely, the disclosed soft
calibration models and/or techniques advantageously generate
adjusted and/or modified projection weights such that the distance
and/or deviation between the estimated totals and the reference
and/or benchmark totals is smaller than some particular value
(e.g., a threshold and/or budget). By relaxing the benchmark
constraints associated with traditional hard calibration models
and/or techniques, the disclosed soft calibration models and/or
techniques advantageously reduce (e.g., eliminate) the
above-described errors that may arise in connection with the use of
hard calibration models and/or techniques when the calibration
weights take on a relatively large magnitude. Thus, a data
measurement company implementing the disclosed soft calibration
models and/or techniques in lieu of traditional hard calibration
models and/or techniques may advantageously provide and/or generate
calibrated panelist and/or reporting data that more closely matches
and/or resembles reference and/or benchmark data.
[0017] In some examples, the apparatus, systems and methods
disclosed herein for calibrating data using relaxed benchmark
constraints determine a set of calibrated weights (e.g., calibrated
projection weights to be applied to panelist and/or reporting data)
based in part on criteria-based input data to be incorporated into
a soft calibration model. In some examples, the criteria-based
input data provides inputs for a target loss function of the soft
calibration model.
[0018] In some examples, the criteria-based input data may include
criteria associated with panelist and/or reporting data, criteria
variables for the criteria, targets for the criteria variables,
lower bounds for the criteria variables, upper bounds for the
criteria variables, scaling parameters for the criteria variables,
and/or importance parameters for the criteria variables. As used
herein, the terms "criterion" and/or "criteria" refer to one or
more panelist and/or reporting data point(s) to be taken into
account when executing and/or performing a calibration model and/or
technique. In some examples, the criteria may be identified by a
unique set of names and/or characters. In other examples, the
criteria may be identified by a unique set of numbers. An example
indexed set of criteria (M) may be expressed and/or defined as
follows:
M={k.di-elect cons..sub.>0:k<=m} Equation 1:
where k represents a dummy variable, .sub.>0 represents the set
of strictly positive natural numbers (e.g., excluding 0), and m
represents the number of criteria.
[0019] In some examples, a set of criteria variables represents
panelist and/or reporting values for each criterion. An example set
of criteria variables (y) may be expressed and/or defined in scalar
and vector notation as follows:
y.sub.j.di-elect cons..A-inverted.j.di-elect cons.M
or: y.di-elect cons..sup.m Equation 2:
where represents real numbers.
[0020] In the setting of soft calibration, the criteria variables
are not identified and/or made to be equal to any specific
prescribed value. Instead, the criteria variables are identified
and/or made to be as close as possible to a set of ideal values
(e.g., reference and/or benchmark data values). As used herein, the
terms "target" and/or "criteria target" refer to an ideal value
associated with a criteria variable. Targets for the criteria
variables are to be provided as input parameters to the soft
calibration model. An example set of targets (t) may be expressed
and/or defined as follows:
t.sub.j.di-elect cons..sub.>0.A-inverted.j.di-elect cons.M or:
t.di-elect cons..sub.>0.sup.m Equation 3:
[0021] In some examples, an upper bound and a lower bound may
additionally be associated with each criteria variable. The upper
bound may be a non-negative number that is greater than or equal to
the corresponding target. The lower bound may be a non-negative
number that is smaller than or equal to the corresponding target.
Setting both the upper and lower bounds equal to the corresponding
target causes the soft calibration model and/or technique to mimic
a traditional hard calibration model and/or technique. Conversely,
setting the lower bound to zero (0) and the upper bound to a large
multiple of the target may result in the lower and upper bounds
being practically inactive.
[0022] In some examples, the upper and lower bounds associated with
respective ones of the criteria variables and/or targets are
identified independently. Thus, some criteria variables may be
required to match their corresponding targets exactly, while others
criteria variables may have very loose bounds relative to their
corresponding targets. Upper and lower bounds for a set of criteria
variables are to be supplied as input parameters to the soft
calibration model. An example set of constraints corresponding to
upper bounds (u) and lower bounds (l) to be associated with a set
of criteria variables (y) and/or targets (t) may be expressed
and/or defined as follows:
l.sub.j.sup.y.ltoreq.y.sub.j.ltoreq.u.sub.j.sup.y:
l.sub.j.sup.y,u.sub.j.sup.y.di-elect
cons..sub..gtoreq.0,l.sub.j.sup.y.ltoreq.t.sub.j,t.sub.j.ltoreq.u.sub.j.s-
up.y.A-inverted.j.di-elect cons.M
or: l.sup.yyu.sup.y: l.sup.y,u.sup.y.di-elect
cons..sub..gtoreq.0.sup.m,l.sup.yt,tu.sup.y Equation 4:
[0023] In some examples, respective ones of the targets to be
associated with corresponding ones of the criteria variables may
have different measurement scales and/or units. For example,
demographic targets measured in terms of a number of people in a
group may be mixed together with purchased amount targets measured
in terms of a local currency. To enable computation of a reasonable
target loss, these different scales and/or units of measurement may
be converted to measureless comparable quantities. In some
examples, such a conversion may be based on relative distances
(e.g., ((y.sub.i-t.sub.i)/t.sub.i)) between respective ones of the
targets and corresponding ones of the criteria variables. In other
examples, a scaling parameter (c) may be applied to respective ones
of the criteria variables. Each scaling parameter (c) may be based
on a relative standard error (rse) associated with the target (t)
corresponding to the respective criteria variable (e.g.
c.sub.i=rse.sub.it.sub.i). In examples described herein, the
scaling parameters have positive values. Example scaling parameters
(c) per criteria variable for computing target loss may be
expressed and/or defined as follows:
c.sub.j.di-elect cons..sub.>0.A-inverted.j.di-elect cons.M or:
c.di-elect cons..sub.>0.sup.m Equation 5:
[0024] In some examples, an importance parameter (v) may be applied
to respective ones of the scaled criteria variables. The importance
parameters may capture and/or represent preferences associated with
respective ones of the scaled criteria variables. In some examples,
each importance parameter (v) may be based on a monotonically
increasing concave function of the corresponding target (t)
( e . g . , v i := t i 4 ) . ##EQU00001##
In examples described herein, the importance parameters have
positive values. Example importance parameters (v) per criteria
variable for computing target loss may be expressed and/or defined
as follows:
v.sub.j.di-elect cons..sub.>0.A-inverted.j.di-elect cons.M or:
v.di-elect cons..sub.>0.sup.m Equation 6:
[0025] In some examples, the criteria-based input data (e.g.,
criteria associated with panelist and/or reporting data, criteria
variables, targets for the criteria variables, lower bounds for the
criteria variables, upper bounds for the criteria variables,
scaling parameters for the criteria variables, and importance
parameters for the criteria variables) may be provided by, accessed
from, and/or stored in a tab-separated values (TSV) file having
multiple columns. For example, a first column of a TSV file for the
criteria-based input data may include identifiers (e.g., a set of
unique names and/or characters) for each criterion. A second column
of the TSV file for the criteria-based input data may include
values (e.g., double precision numerical values) for each target. A
third column of the TSV file for the criteria-based input data may
include values (e.g., double precision numerical values) for each
lower bound. A fourth column of the TSV file for the criteria-based
input data may include values (e.g., double precision numerical
values) for each upper bound. A fifth column of the TSV file for
the criteria-based input data may include values (e.g., double
precision numerical values) for each scaling parameter. A sixth
column of the TSV file for the criteria-based input data may
include values (e.g., double precision numerical values) for each
importance parameter. In such an example, the respective values of
the second column of the TSV file are greater than or equal to
corresponding ones of the respective values of the third column of
the TSV file, and less than or equal to corresponding ones of the
respective values of the fourth column of the TSV file. In some
such examples, the respective values of the fifth column and the
sixth column of the TSV file are positive, and cannot be zero
(0).
[0026] In other examples, the criteria-based input data may be
provided by, accessed from, and/or stored in a file having a format
that differs from that of a TSV file. For example, the
criteria-based input data may be provided by, accessed from, and/or
stored in a comma-separated values (CSV) file, or some other type
of data file.
[0027] In response to identifying and/or determining the
criteria-based input data (e.g., criteria associated with panelist
and/or reporting data, criteria variables, targets for the criteria
variables, lower bounds for the criteria variables, upper bounds
for the criteria variables, scaling parameters for the criteria
variables, and importance parameters for the criteria variables),
distances between respective ones of the panelist and/or reporting
values captured by the criteria variables (y), and corresponding
respective ones of the targets (t), may be measured and/or
determined. As used herein, the term "target loss" refers to a
measured distance between (a) a panelist and/or reporting value
captured by a criteria variable, and (b) a corresponding target. In
some examples, target loss may be expressed and/or defined in terms
of a target loss function (F(y)). In some examples, it is desired
that the target loss function (F(y)) will express a weighted
average of criteria variable distances while at the same time being
robust with respect to outliers. Thus, it may be desired that the
target loss function (F(y)) is both convex and robust.
[0028] In some examples, the target loss function (F(y)) may be
based on a known Huber loss function (H.sub..PHI.( )). For example,
the target loss function (F(y)) may be expressed and/or defined as
follows:
F : .gtoreq. 0 m .fwdarw. .gtoreq. 0 { .infin. } .times. F
.function. ( y ) = { .function. ( y ) for .times. I y y u y ,
.infin. , otherwise . .times. ( y j ) j .di-elect cons. M 1 j
.di-elect cons. M v j .times. j .di-elect cons. M v j .times. H
.PHI. ( y j - t j c j ) .times. y v , H .PHI. ( diag .function. ( c
) - 1 .times. ( y - t ) ) v , 1 m Equation .times. 7
##EQU00002##
where H.sub..PHI.( ) is the Huber loss function expressed and/or
defined as follows:
H .PHI. ( z ) = { 1 2 .times. z 2 for .times.
"\[LeftBracketingBar]" z "\[RightBracketingBar]" .ltoreq. .PHI. ,
.PHI. .function. ( "\[LeftBracketingBar]" z "\[RightBracketingBar]"
- 1 2 .times. .PHI. ) , otherwise . ##EQU00003##
[0029] Replacing the scalar (z) of the Huber loss function with a
vector (z) results in (H.sub..PHI.(z)) being applied for each
component of (z) with the same value of the parameter .PHI.. In
such an example, (H.sub..PHI.(Z)) is of the same dimensionality as
(z).
[0030] In some examples, the apparatus, systems and methods
disclosed herein for calibrating data using relaxed benchmark
constraints determine a set of calibrated weights (e.g., calibrated
projection weights to be applied to panelist and/or reporting data)
based in part on unit-based input data to be incorporated into the
soft calibration model. In some examples the unit-based input data
provides inputs for a weight loss function of the soft calibration
model.
[0031] In some examples, the unit-based input data may include
units associated with panelist and/or reporting data, unit
variables for the units, initial weights for the unit variables,
lower bounds for the unit variables, upper bounds for the unit
variables, and/or size parameters for the unit variables. As used
herein, the term "unit" refers to one or more projection weight(s)
to be used and/or calibrated to attain one or more corresponding
panelist and/or reporting data point(s) relative to one or more
corresponding target(s) when executing and/or performing a
calibration model and/or technique. In some examples, the units may
be identified by a unique set of names and/or characters. In other
examples, the units may be identified by a unique set of numbers.
An example indexed set of units (N) may be expressed and/or defined
as follows:
N={k.di-elect cons..sub.>0:k<=n} Equation 8:
where k represents a dummy variable, .sub.>0 represents the set
of strictly positive natural numbers (e.g., excluding 0), and n
represents the number of units.
[0032] In some examples, a set of unit variables represents the
calibrated weight for each unit. An example set of unit variables
(x) may be expressed and/or defined in scalar and vector notation
as follows:
x.sub.i.di-elect cons..A-inverted.i.di-elect cons.N
or: x.di-elect cons..sup.n Equation 9:
where represents real numbers.
[0033] Unlike the above-described criteria variables that are made
to be as close as possible to the above-described targets, there is
no corresponding set of ideal values (e.g., reference and/or
benchmark data values) for respective ones of the unit variables.
Instead, respective ones of the unit variables are associated with
corresponding respective ones of initial weights that are to be
adjusted as little as possible. In some examples, respective ones
of the initial weights may assume different roles in different
domains (e.g., coverage adjustment, weights derived by panel
design, etc.). Initial weights for the unit variables are to be
supplied as input parameters to the soft calibration model. An
example set of initial weights (x.sup.o) may be expressed and/or
defined as follows:
x.sub.i.sup.0.di-elect cons..sub.>0.A-inverted.i.di-elect cons.N
or: x.sup.0.di-elect cons..sub.>0.sup.n Equation 10:
[0034] In some examples, an upper bound and a lower bound may
additionally be associated with each unit variable. The upper bound
may be a non-negative number that is greater than or equal to the
corresponding initial weight. The lower bound may be a non-negative
number that is smaller than or equal to the corresponding initial
weight. In some examples, the lower bound may be set to zero (0)
and the upper bound may be set to a large multiple of the initial
weight. In other examples, the lower bound and the upper bound may
respectively be determined by dividing (for the lower bound) and/or
multiplying (for the upper bound) the initial weight by a
constant.
[0035] In some examples, the upper and lower bounds associated with
respective ones of the unit variables and/or initial weights are
identified independently. Upper and lower bounds for the unit
variables are to be supplied as input parameters to the soft
calibration model. An example set of constraints corresponding to
upper bounds (u) and lower bounds (l) to be associated with a set
of unit variables (x) and/or initial weights (x.sup.o) may be
expressed and/or defined as follows:
l.sub.i.sup.x.ltoreq.x.sub.i.ltoreq.u.sub.i.sup.x:
l.sub.i.sup.x,u.sub.i.sup.x.di-elect
cons..sub..gtoreq.0,l.sub.i.sup.x.ltoreq.x.sub.i.sup.0.ltoreq.u.sub.i.sup-
.x.A-inverted.i.di-elect cons.N
or: l.sup.xxu.sup.x: l.sup.x,u.sup.x.di-elect
cons..sub..gtoreq.0.sup.n,l.sup.xx.sup.0u.sup.x Equation 11:
[0036] Unlike respective ones of the targets to be associated with
corresponding ones of the criteria variables described above,
respective ones of the initial weights associated with
corresponding respective ones of the unit variables do not have
different measurement scales and/or units. Accordingly, there is no
need to convert differing scales and/or units of measurement to
measureless comparable quantities in connection with computing
weight loss.
[0037] In some examples, a size parameter (s) may be applied to
respective ones of the unit variables. The size parameters may
capture and/or represent preferences associated with respective
ones of the unit variables. In some examples, each size parameter
(s) may be based on an average of non-zero contributions of a unit
to the criteria. In examples described herein, the size parameters
have positive values. Example size parameters (s) per unit variable
for computing weight loss may be expressed and/or defined as
follows:
s.sub.i.di-elect cons..sub.>0.A-inverted.i.di-elect cons.N or:
s.di-elect cons..sub.>0.sup.n Equation 12:
[0038] In some examples, the unit-based input data (e.g., units
associated with panelist and/or reporting data, unit variables for
the units, initial weights for unit variables, lower bounds for
unit variables, upper bounds for unit variables, and size
parameters for unit variables) may be provided by, accessed from,
and/or stored in a TSV file having multiple columns. For example, a
first column of a TSV file for the unit-based input data may
include identifiers (e.g., a set of unique names and/or characters)
for each unit. A second column of the TSV file for the unit-based
input data may include values (e.g., double precision numerical
values) for each initial weight. A third column of the TSV file for
the unit-based input data may include values (e.g., double
precision numerical values) for each lower bound. A fourth column
of the TSV file for the unit-based input data may include values
(e.g., double precision numerical values) for each upper bound. A
fifth column of the TSV file for the unit-based input data may
include values (e.g., double precision numerical values) for each
size parameter. In such an example, the respective values of the
second column of the TSV file are greater than or equal to
corresponding ones of the respective values of the third column of
the TSV file, and less than or equal to corresponding ones of the
respective values of the fourth column of the TSV file. In some
such examples, the respective values of the fifth column of the TSV
file are positive, and cannot be zero (0).
[0039] In other examples, the unit-based input data may be provided
by, accessed from, and/or stored in a file having a format that
differs from that of a TSV file. For example, the unit-based input
data may be provided by, accessed from, and/or stored in a CSV
file, or some other type of data file.
[0040] In response to identifying and/or determining the unit-based
input data (e.g., units associated with panelist and/or reporting
data, unit variables for the units, initial weights for unit
variables, lower bounds for unit variables, upper bounds for unit
variables, and size parameters for unit variables), distances
between respective ones of the currently evaluated weights captured
by the unit variables (x), and corresponding respective ones of the
initial weights)(x.degree., may be measured and/or determined. As
used herein, the term "weight loss" refers to a measured distance
between (a) an evaluated weight captured by a unit variable, and
(b) a corresponding initial weight. In some examples, weight loss
may be expressed and/or defined in terms of a weight loss function
(G(x)). In some examples, it is desired that the weight loss
function (G(x)) express a weighted average of unit variable
distances. For example, the weight loss function (G(x)) may be
expressed and/or defined as follows:
G : .gtoreq. 0 n .fwdarw. .gtoreq. 0 { .infin. } .times. G
.function. ( x ) = { .function. ( x ) for .times. I x x u x ,
.infin. , otherwise . .times. ( x i ) i .di-elect cons. N 1 i
.di-elect cons. N s i .times. x i 0 .times. i .di-elect cons. N s i
.times. x i 0 ( x i x i 0 - 1 ) 2 .times. x diag .function. ( x 0 )
.times. s , ( diag .function. ( x 0 ) - 1 .times. x - 1 n ) 2 x 0 ,
s Equation .times. 13 ##EQU00004##
[0041] In some examples, the apparatus, systems and methods
disclosed herein for calibrating data using relaxed benchmark
constraints determine a set of calibrated weights (e.g., calibrated
projection weights to be applied to panelist and/or reporting data)
based in part on matrix data to be incorporated into the soft
calibration model. In some examples, a design matrix including the
matrix data may be generated and/or derived from the criteria-based
input data and the unit-based input data. The design matrix may
capture and/or generate relationships between the above-described
units and the above-described criteria. For example, the
non-expanded contribution of each unit to each criterion may be
captured by a design matrix having non-negative entries. An example
design matrix may be expressed and/or defined as follows:
(a.sub.ij).sub.i.di-elect cons.N,j.di-elect
cons.M,a.sub.ij.di-elect cons..sub..gtoreq.0.A-inverted.i.di-elect
cons.N.A-inverted.j.di-elect cons.M
A.di-elect cons..sub..gtoreq.0.sup.n.times.m Equation 14:
[0042] Accordingly, an example relationship formula for
relationships between units and criteria may be expressed and/or
defined as follows:
Relationship .times. i .di-elect cons. N a ij .times. x i = y j
.times. .A-inverted. j .di-elect cons. M .times. Matrix .times.
Notation .times. Ax = y Equation .times. 15 ##EQU00005##
[0043] In some examples, the design matrix may be provided by,
accessed from, and/or stored in a TSV file having multiple columns.
For example, a first column of a TSV file for the design matrix may
include identifiers (e.g., a set of unique names and/or characters)
corresponding to the first column of the above-described TSV file
for the unit-based input data. A second column of the TSV file for
the design matrix may include identifiers (e.g., a set of unique
names and/or characters) corresponding to the first column of the
above-described TSV file for the criteria-based input data. A third
column of the TSV file for the design matrix may include values
(e.g., double precision numerical values) for the contribution of
respective ones of the units to respective ones of the criteria
without weighting. In such an example, the respective values of the
third column of the TSV file for the design matrix are positive and
not equal to zero (0). In some such examples, if there is no record
for a given pair of unit and criteria identifiers in the TSV file
for the design matrix, the data is assumed to be zero (0).
[0044] In other examples, the design matrix may be provided by,
accessed from, and/or stored in a file having a format that differs
from that of a TSV file. For example, the design matrix may be
provided by, accessed from, and/or stored in a CSV file, or some
other type of data file.
[0045] In some examples, the apparatus, systems and methods
disclosed herein for calibrating data using relaxed benchmark
constraints determine a set of calibrated weights (e.g., calibrated
projection weights to be applied to panelist and/or reporting data)
based in part on model parameter data to be incorporated into the
soft calibration model. In some examples, the model parameter data
includes a Huber function parameter associated with target loss and
a budget parameter associated with weight loss. As described above
in connection with the target loss function of Equation 7, a Huber
loss function H.sub..PHI.( ) may be implemented to measure the
distance between (a) a panelist and/or reporting value captured by
a criteria variable, and (b) a corresponding target. The Huber loss
function is parametric in .PHI.. Identification of a Huber function
parameter (.PHI.) applicable across all criteria enables a fixed
target loss to be computed.
[0046] Target loss and the weight loss are conflicting objectives
of the soft calibration process. For example, the smaller that the
value of the target loss becomes, the larger that the value of the
weight loss becomes by necessity, and vice-versa. In some examples,
to obtain a unique solution, the target loss may be minimized and a
constraint may be placed on the value that the weight loss is
allowed to obtain. As used herein, the term "budget" refers to a
constraint placed on the value that the weight loss is allowed to
obtain. In some examples, a budget parameter (.theta.) is an upper
bound (e.g., .theta..di-elect cons..sub.>0) associated with the
weight loss. An example constraint corresponding to the budget
parameter (.theta.) may be expressed and/or defined as follows:
G(x).ltoreq..theta. for .theta..di-elect cons..sub.>0 Equation
16:
[0047] Based on the above-described criteria-based input data
(e.g., criteria associated with panelist and/or reporting data,
criteria variables for the criteria, targets for the criteria
variables, lower bounds for the criteria variables, upper bounds
for the criteria variables, scaling parameters for the criteria
variables, and importance parameters for the criteria variables),
target loss function, unit-based input data (e.g., units associated
with panelist and/or reporting data, unit variables for the units,
initial weights for the unit variables, lower bounds for the unit
variables, upper bounds for the unit variables, and size parameters
for the unit variables), weight loss function, matrix data, and
model parameter data, an example calibration model to calibrate
data using relaxed benchmark constraints (e.g., an example soft
calibration model) may be expressed and/or defined as follows:
min F(y)
subject to: Ax=y
l.sub.xxu.sup.x
l.sup.yyu.sup.y
G(x).ltoreq..theta. Equation 17:
[0048] The soft calibration model of Equation 17 may be implemented
and/or executed to provide a unique solution whereby respective
calibrated panelist and/or reporting values from among a set of
calibrated panelist and/or reporting values are close in value to,
but not necessarily equal to, respective target and/or benchmark
values from among a corresponding set of target and/or benchmark
values. Implementation and/or execution of the soft calibration
model of Equation 17 also results in a determination and/or
identification of the calibrated weights (e.g., optimized weights).
As the initial weights (x.sup.o) are known and fixed, the
calibrated weights may be identified and/or determined based on the
weight adjustments per unit
x i x i 0 . ##EQU00006##
[0049] In some examples, calibrated weights determined as a result
of executing the soft calibration model of Equation 17 may be
provided by, accessed from, and/or stored in a TSV file having
multiple columns. For example, a first column of a TSV file for the
calibrated weights may include identifiers (e.g., a set of unique
names and/or characters) corresponding to the first column of the
above-described TSV file for the unit-based input data. A second
column of the TSV file for the calibrated weights may include
values (e.g., double precision numerical values) for the weight
adjustment (x.sup.adj) of each unit or, alternatively, the
calibrated weight of each unit. In other examples, calibrated
weights determined as a result of executing the soft calibration
model of Equation 17 may be provided by, accessed from, and/or
stored in a file having a format that differs from that of a TSV
file. For example, calibrated weights determined as a result of
executing the soft calibration model of Equation 17 may be provided
by, accessed from, and/or stored in a CSV file, or some other type
of data file.
[0050] Table 1 below provides an example of panelist and/or
reporting data to be calibrated:
TABLE-US-00001 TABLE 1 AgeGroup Sex Population RetailerA RetailerB
15-34 Male 40199347 28.68 1.28 35-54 Male 40945028 82.78 2.32 55+
Male 26054981 21.72 0.46 15-34 Female 38876268 27.97 1.82 35-54
Female 41881451 37.10 2.00 55+ Female 33211456 13.82 0.42
[0051] The panelist and/or reporting data of Table 1 includes two
demographic dimensions: (1) an age group dimension having three
levels; and (2) a sex dimension having two levels. A population
estimate is provided for each intersection of age and group
dimensions. The panelist and/or reporting data of Table 1 also
includes the average spending per person for two retailers (e.g.,
RetailerA and RetailerB).
[0052] Criteria-based input data may be associated with the
panelist and/or reporting data of Table 1 above. For example, Table
2 below provides an example of criteria-based input data associated
with the panelist and/or reporting data of Table 1 in a scenario
where the scaling parameters (c) described above in connection with
Equation 5 have been set to equal the corresponding targets (t),
and where the importance parameters (v) described above in
connection with Equation 6 have been set to a value of 1.00 for the
demographic targets:
TABLE-US-00002 TABLE 2 criteria ID target ly uy V c demo::Sex::Male
107199356 107199356 107199356 1.00 107199356 demo::Sex::Female
113969175 113969175 113969175 1.00 113969175 demo::AgeGroup::15-34
79075615 79075615 79075615 1.00 79075615 demo::AgeGroup::35-54
82826479 82826479 82826479 1.00 82826479 demo::AgeGroup::55+
59266437 59266437 59266437 1.00 59266437 volumetric::RetailerA
9029255672 6566731398 9850097097 90600.30 8208414247
volumetric::RetailerB 310554470 261519553 392279330 18080.36
326899442
[0053] Unit-based input data may also be associated with the
panelist and/or reporting data of Table 1 above. For example, Table
3 below provides an example of unit-based input data associated
with the panelist and/or reporting data of Table 1 in a scenario
where the initial weights (x.sup.0) are set to equal the population
estimates of the panelist and/or reporting data at intersection
level:
TABLE-US-00003 TABLE 3 unit ID x0 lx ux size 15-34::Male 40199347
20099674 80398694 29.96 35-54::Male 40945028 20472514 81890056
85.10 55+::Male 26054981 13027491 52109962 22.18 15-34::Female
38876268 19438134 77752536 29.79 35-54::Female 41881451 20940726
83762902 39.10 55+::Female 33211456 16605728 66422912 14.24
[0054] Table 4 below provides an example of a design matrix
including matrix data associated with the criteria-based input data
of Table 2 above and the unit-based input data of Table 3
above:
TABLE-US-00004 TABLE 4 unit ID criteria ID a 15-34::Male
demo::Sex::Male 1.00 35-54::Male demo::Sex::Male 1.00 55+::Male
demo::Sex::Male 1.00 15-34::Female demo::Sex::Female 1.00
35-54::Female demo::Sex::Female 1.00 55+::Female demo::Sex::Female
1.00 15-34::Male demo::AgeGroup::15-34 1.00 35-54::Male
demo::AgeGroup::35-54 1.00 55+::Male demo::AgeGroup::55+ 1.00
15-34::Female demo::AgeGroup::15-34 1.00 35-54::Female
demo::AgeGroup::35-54 1.00 55+::Female demo::AgeGroup::55+ 1.00
15-34::Male volumetric::RetailerA 28.68 35-54::Male
volumetric::RetailerA 82.78 55+::Male volumetric::RetailerA 21.72
15-34::Female volumetric::RetailerA 27.97 35-54::Female
volumetric::RetailerA 37.10 55+::Female volumetric::RetailerA 13.82
15-34::Male volumetric::RetailerB 1.28 35-54::Male
volumetric::RetailerB 2.32 55+::Male volumetric::RetailerB 0.46
15-34::Female volumetric::RetailerB 1.82 35-54::Female
volumetric::RetailerB 2.00 55+::Female volumetric::RetailerB
0.42
[0055] Table 5 below provides an example of calibrated weights data
resulting from executing the soft calibration model of Equation 17
based in part on the criteria-based input data of Table 2, the
unit-based input data of Table 3, and the matrix data of Table 4,
in a scenario where the budget parameter (.theta.) has been set to
a value of 0.35 and the Huber function parameter (.PHI.) has been
set to a value of 0.50:
TABLE-US-00005 TABLE 5 unit ID xadj 15-34::Male 0.8789425
35-54::Male 1.4060901 55+::Male 0.5486109 15-34::Female 1.1251775
35-54::Female 0.6029897 55+::Female 1.3541228
[0056] In some circumstances, execution of the soft calibration
model of Equation 17 described above may result in the soft
calibration model performing in an unexpected manner. One such set
of circumstances occurs when two conditions are present: (1) the
target loss function (F(y)) has a flat region (D) (e.g., a flat
region (D) expressed and/or defined as
.E-backward.D.sub..gtoreq.0.sup.m: y.sub.1,y.sub.2.di-elect
cons.D|F(y.sub.i)-F(y.sub.2)|.apprxeq.0); and (2) the budget
parameter (.theta.) is large enough to allow the minimization
procedure of the soft calibration model of Equation 17 to reach the
flat region (D) of the target loss function (F(y)).
[0057] For example, in the case of a totally flat region (D) (e.g.,
where |F(y.sub.1)-F(y.sub.2)|=0 in condition (1) above), the soft
calibration model of Equation 17 does not specify which one of the
countless possibilities is to be preferred. Different solvers might
choose to implement heuristics picking up one of the edges of the
optimal set or, alternatively, a central point of this set. A
particular case is when there is a totally flat optimal region for
the target loss and all criteria are fulfilled exactly (e.g., where
y.di-elect cons.DF(y)=0). This particular case reduces the soft
calibration problem to the traditional case of statistical weight
calibration. Yet, unlike the traditional calibration approach, the
soft calibration model of Equation 17 does not capture a preference
for a solution that minimizes the weight loss. As another example,
in the case of a nearly flat region (D) (e.g., where
|F(y.sub.1)-F(y.sub.2)| is negligible and/or close to machine
precision), implementation heuristics become unreliable, and may
result in a progressively increasing weight loss function (G(x))
that provides no meaningful improvement in relation to the target
attainment. In some such examples, execution of the soft
calibration model may result in calibrated weights that do not
provide a unique solution for the executed soft calibration
model.
[0058] In some examples, a stability parameter (.gamma.) may be
incorporated into (e.g., appended to) the soft calibration model of
Equation 17 to remedy and/or prevent unexpected performance of the
soft calibration model resulting from the above-described
circumstances and/or conditions. The stability parameter (.gamma.)
reduces the influence of the budget parameter (.theta.) on the soft
calibration model. For example, incorporation of the stability
parameter (.gamma.) may prevent the minimization procedure of the
soft calibration model of Equation 17 from reaching the flat region
(D) of the target loss function (F(y)). In some examples, the
stability parameter (.gamma.) is included as part of the model
parameter data described above. In some examples, the stability
parameter (.gamma.) may be incorporated into the soft calibration
model of Equation 17 by adding the product of the stability
parameter (.gamma.) and the weight loss function (G(x)) to the
target loss function (F(y)). In such examples, the revised soft
calibration model may be expressed and/or defined as follows:
min F(y)+.gamma.G(x)
subject to: Ax=y
l.sub.xxu.sup.x
l.sup.yyu.sup.y
G(x).ltoreq..theta. Equation 18:
[0059] In some examples, the stability parameter (.gamma.) may be
determined and/or provided at run-time. As the target loss function
(F(y)) and the weight loss function (G(x)) are both scaled to be
measureless (e.g. both are non-negative, and both are expected to
be not much larger than 1), the stability parameter (.gamma.) may
preferably have a value between 0.00001 and 0.01 (e.g., comparable
to a precision sensitivity associated with the soft calibration
model). In some examples, the value of the stability parameter
(.gamma.) may be increased until the calibrated weights that result
from executing the soft calibration model provide a unique solution
for the soft calibration model. Thus, implementation and/or
incorporation of the stability parameter (.gamma.) may reduce the
occurrence of errors (e.g., the generation of calibrated weights
providing non-unique solutions) attributable to and/or arising from
an influence of the value of the budget parameter (.theta.) on the
soft calibration model.
[0060] The soft calibration model of Equation 18 may be implemented
and/or executed to provide a unique solution whereby respective
calibrated panelist and/or reporting values from among a set of
calibrated panelist and/or reporting values are close in value to,
but not necessarily equal to, respective target and/or benchmark
values from among a corresponding set of target and/or benchmark
values. Implementation and/or execution of the soft calibration
model of Equation 18 also results in a determination and/or
identification of the calibrated weights (e.g., optimized weights).
As the initial weights (x.sup.0) are known and fixed, the
calibrated weights may be identified and/or determined based on the
weight adjustments per unit
x i x i 0 . ##EQU00007##
[0061] In some examples, calibrated weights determined as a result
of executing the soft calibration model of Equation 18 may be
provided by, accessed from, and/or stored in a TSV file having
multiple columns. For example, a first column of a TSV file for the
calibrated weights may include identifiers (e.g., a set of unique
names and/or characters) corresponding to the first column of the
above-described TSV file for the unit-based input data. A second
column of the TSV file for the calibrated weights may include
values (e.g., double precision numerical values) for the weight
adjustment of each unit or, alternatively, the calibrated weight of
each unit. In other examples, calibrated weights determined as a
result of executing the soft calibration model of Equation 18 may
be provided by, accessed from, and/or stored in a file having a
format that differs from that of a TSV file. For example,
calibrated weights determined as a result of executing the soft
calibration model of Equation 18 may be provided by, accessed from,
and/or stored in a CSV file, or some other type of data file.
[0062] FIG. 1 is a block diagram of an example calibration
apparatus 100 constructed in accordance with the teachings of this
disclosure. The calibration apparatus 100 of FIG. 1 may be
implemented to calibrate panelist and/or reporting data using
relaxed benchmark constraints incorporated into a soft calibration
model (e.g., the example soft calibration model of Equation 17 or
the example soft calibration model of Equation 18 described above).
In the illustrated example of FIG. 1, the calibration apparatus 100
includes an example criteria-based input determiner 102, an example
unit-based input determiner 104, an example matrix determiner 106,
an example model parameter determiner 108, an example calibration
engine 110, an example user interface 112, and an example memory
114.
[0063] The example criteria-based input determiner 102 of FIG. 1
determines and/or identifies example criteria-based input data 118
to be incorporated into an example target loss function 120 of a
soft calibration model to be executed by the example calibration
engine 110 of the calibration apparatus 100 of FIG. 1. The
criteria-based input data 118 determined and/or identified by the
criteria-based input determiner 102 may be of any type, form and/or
format (e.g., a TSV file, a CSV file, etc.), and may be stored in a
computer-readable storage medium such as the example memory 114 of
FIG. 1 described below. In some examples, the criteria-based input
determiner 102 of FIG. 1 determines and/or identifies the
criteria-based input data 118 by accessing and/or obtaining the
criteria-based input data 118 from the memory 114 of FIG. 1. In
other examples, the criteria-based input determiner 102 of FIG. 1
determines and/or identifies criteria-based input data 118 received
from the example user interface 112 of FIG. 1 described below. In
such other examples, the criteria-based input determiner 102 of
FIG. 1 may cause the memory 114 of FIG. 1 to store the received
criteria-based input data 118.
[0064] In some examples, the criteria-based input data 118 to be
determined and/or identified by the criteria-based input determiner
102 of FIG. 1 may include criteria associated with example panelist
and/or reporting data (e.g., survey data) 116, criteria variables
for the criteria, targets for the criteria variables, lower bounds
for the criteria variables, upper bounds for the criteria
variables, scaling parameters for the criteria variables, and/or
importance parameters for the criteria variables. In some examples,
the criteria of the criteria-based input data 118 may be expressed
in a manner consistent with Equation 1 described above. In some
examples, the criteria variables of the criteria-based input data
118 may be expressed in a manner consistent with Equation 2
described above. In some examples, the targets of the
criteria-based input data 118 may be expressed in a manner
consistent with Equation 3 described above. In some examples, the
lower and upper bounds of the criteria-based input data 118 may be
expressed in a manner consistent with Equation 4 described above.
In some examples, the scaling parameters of the criteria-based
input data 118 may be expressed in a manner consistent with
Equation 5 described above. In some examples, the importance
parameters of the criteria-based input data 118 may be expressed in
a manner consistent with Equation 6 described above. In some
examples, the target loss function 120 into which the
criteria-based input data 118 determined and/or identified by the
criteria-based input determiner 102 of FIG. 1 is to be incorporated
may be expressed in a manner consistent with Equation 7 described
above.
[0065] The example unit-based input determiner 104 of FIG. 1
determines and/or identifies example unit-based input data 122 to
be incorporated into an example weight loss function 124 of the
soft calibration model to be executed by the example calibration
engine 110 of the calibration apparatus 100 of FIG. 1. The
unit-based input data 122 determined and/or identified by the
unit-based input determiner 104 may be of any type, form and/or
format (e.g., a TSV file, a CSV file, etc.), and may be stored in a
computer-readable storage medium such as the example memory 114 of
FIG. 1 described below. In some examples, the unit-based input
determiner 104 of FIG. 1 determines and/or identifies the
unit-based input data 122 by accessing and/or obtaining the
unit-based input data 122 from the memory 114 of FIG. 1. In other
examples, the unit-based input determiner 104 of FIG. 1 determines
and/or identifies unit-based input data 122 received from the
example user interface 112 of FIG. 1 described below. In such other
examples, the unit-based input determiner 104 of FIG. 1 may cause
the memory 114 of FIG. 1 to store the received unit-based input
data 122.
[0066] In some examples, the unit-based input data 122 to be
determined and/or identified by the unit-based input determiner 104
of FIG. 1 may include units associated with the panelist and/or
reporting data 116, unit variables for the units, initial weights
for the unit variables, lower bounds for the unit variables, upper
bounds for the unit variables, and/or size parameters for the unit
variables. In some examples, the units of the unit-based input data
122 may be expressed in a manner consistent with Equation 8
described above. In some examples, the unit variables of the
unit-based input data 122 may be expressed in a manner consistent
with Equation 9 described above. In some examples, the initial
weights of the unit-based input data 122 may be expressed in a
manner consistent with Equation 10 described above. In some
examples, the lower and upper bounds of the unit-based input data
122 may be expressed in a manner consistent with Equation 11
described above. In some examples, the size parameters of the
unit-based input data 122 may be expressed in a manner consistent
with Equation 12 described above. In some examples, the weight loss
function 124 into which the unit-based input data 122 determined
and/or identified by the unit-based input determiner 104 of FIG. 1
is to be incorporated may be expressed in a manner consistent with
Equation 13 described above.
[0067] The example matrix determiner 106 of FIG. 1 determines,
generates, derives and/or identifies example matrix data 126 to be
incorporated into the soft calibration model to be executed by the
example calibration engine 110 of the calibration apparatus 100 of
FIG. 1. The matrix data 126 determined, generated, derived and/or
identified by the matrix determiner 106 of FIG. 1 may be of any
type, form and/or format (e.g., a TSV file, a CSV file, etc.), and
may be stored in a computer-readable storage medium such as the
example memory 114 of FIG. 1 described below. In some examples, the
matrix determiner 106 of FIG. 1 determines and/or identifies the
matrix data 126 by accessing and/or obtaining the matrix data 126
from the memory 114 of FIG. 1. In other examples, the matrix
determiner 106 of FIG. 1 determines and/or identifies matrix data
126 received from the example user interface 112 of FIG. 1
described below. In such other examples, the matrix determiner 106
of FIG. 1 may cause the memory 114 of FIG. 1 to store the received
matrix data 126.
[0068] In some examples, the matrix determiner 106 of FIG. 1
determines, generates, derives and/or identifies the matrix data
126 based on the example criteria-based input data 118 of FIG. 1
and the example unit-based input data 122 of FIG. 1. In some
examples, the matrix data 126 determined, generated derived and/or
identified by the matrix determiner 106 of FIG. 1 may be expressed
in a manner consistent with Equation 14 and/or Equation 15
described above. In some examples, the matrix data 126 determined,
generated, derived and/or identified by the matrix determiner 106
may capture relationships between the criteria of the
criteria-based input data 118 and the units of the unit-based input
data 122. For example, the non-expanded contribution of each unit
to each criterion may be captured by the matrix data 126.
[0069] The example model parameter determiner 108 of FIG. 1
determines and/or identifies example model parameter data 128 to be
incorporated into the soft calibration model to be executed by the
example calibration engine 110 of the calibration apparatus 100 of
FIG. 1. The model parameter data 128 determined and/or identified
by the model parameter determiner 108 of FIG. 1 may be of any type,
form and/or format, and may be stored in a computer-readable
storage medium such as the example memory 114 of FIG. 1 described
below. In some examples, the model parameter determiner 108 of FIG.
1 determines and/or identifies the model parameter data 128 by
accessing and/or obtaining the model parameter data 128 from the
memory 114 of FIG. 1. In other examples, the model parameter
determiner 108 of FIG. 1 determines and/or identifies model
parameter data 128 received from the example user interface 112 of
FIG. 1 described below. In such other examples, the model parameter
determiner 108 of FIG. 1 may cause the memory 114 of FIG. 1 to
store the received model parameter data 128.
[0070] In some examples, the model parameter data 128 to be
determined and/or identified by the model parameter determiner 108
of FIG. 1 may include a Huber function parameter, a budget
parameter, and/or a stability parameter. In some examples, the
budget parameter of the model parameter data 128 determined and/or
identified by the model parameter determiner 108 of FIG. 1 may be
expressed in a manner consistent with Equation 16 described
above.
[0071] The example calibration engine 110 of FIG. 1 builds,
constructs and/or compiles the soft calibration model to be
executed by the calibration apparatus 100. In some examples, the
calibration engine 110 of FIG. 1 builds, constructs and/or compiles
the soft calibration model based on the criteria-based input data
118, the target loss function 120, the unit-based input data 122,
the weight loss function 124, the matrix data 126, and the model
parameter data 128 of FIG. 1. In some examples, the soft
calibration model built, constructed and/or compiled by the
calibration engine 110 of FIG. 1 may be expressed in a manner
consistent with Equation 17 described above. In other examples, the
soft calibration model built, constructed and/or compiled by the
calibration engine 110 of FIG. 1 may be expressed in a manner
consistent with Equation 18 described above. The calibration engine
110 of FIG. 1 executes and/or controls the execution of the built,
constructed and/or compiled soft calibration model.
[0072] In the illustrated example of FIG. 1, the calibration engine
110 includes an example calibrated weights determiner 130. The
calibrated weights determiner 130 of FIG. 1 determines and/or
calculates example calibrated weights data 132 in response to
execution of the soft calibration model by the calibration engine
110. In some examples, in response to the calibration engine 110
executing the soft calibration model, the calibrated weights
determiner 130 of FIG. 1 determines the calibrated weights data 132
based on the criteria-based input data 118, the target loss
function 120, the unit-based input data 122, the weight loss
function 124, the matrix data 126, and the model parameter data 128
incorporated into the executed soft calibration model. In some
examples, the calibrated weights determiner 130 of FIG. 1 may
determine and/or calculate the calibrated weights data 132 based on
adjusted calibration weights output by the soft calibration model.
In some examples, the calibrated weights determiner 130 of FIG. 1
may cause the calibrated weights data 132 to be presented (e.g.,
displayed) via the example user interface 112 of FIG. 1. The
calibrated weights data 132 determined and/or calculated by the
calibrated weights determiner 130 of FIG. 1 may be of any type,
form and/or format (e.g., a TSV file, a CSV file, etc.), and may be
stored in a computer-readable storage medium such as the example
memory 114 of FIG. 1 described below.
[0073] In the illustrated example of FIG. 1, the calibration engine
110 also includes an example calibrated reporting data determiner
134. The example calibrated reporting data determiner 134 of FIG. 1
determines and/or calculates example calibrated panelist and/or
reporting data 136. In some examples, the calibrated panelist
and/or reporting data 136 determined and/or calculated by the
calibrated reporting data determiner 134 of FIG. 1 is based on
initial panelist and/or reporting data (e.g., the panelist and/or
reporting data 116 of FIG. 1) and the calibrated weights data 132
determined and/or calculated by the calibrated weights determiner
130 of FIG. 1. For example, the calibrated reporting data
determiner 134 of FIG. 1 may determine and/or calculate the
calibrated panelist and/or reporting data 136 by applying the
calibrated weights data 132 to the panelist and/or reporting data
116 of FIG. 1. In some examples, the calibrated reporting data
determiner 134 of FIG. 1 may cause the calibrated panelist and/or
reporting data 136 to be presented (e.g., displayed) via the
example user interface 112 of FIG. 1. The calibrated panelist
and/or reporting data 136 determined and/or calculated by the
calibrated reporting data determiner 134 of FIG. 1 may be of any
type, form and/or format (e.g., a TSV file, a CSV file, etc.), and
may be stored in a computer-readable storage medium such as the
example memory 114 of FIG. 1 described below.
[0074] In the illustrated example of FIG. 1, the calibration engine
110 also includes an example calibration model validator 138. The
example calibrated reporting data determiner 134 of FIG. 1
validates the soft calibration model executed by the example
calibration engine 110 of FIG. 1. For example, the calibration
model validator 138 of FIG. 1 may validate the soft calibration
model executed by the calibration engine 110 of FIG. 1 by
determining whether the calibrated weights resulting from execution
of the soft calibration model (e.g., the calibrated weights data
132 determined by the calibrated weights determiner 130 of FIG. 1)
provide a unique solution for the executed soft calibration
model.
[0075] In some examples, if the calibration model validator 138 of
FIG. 1 determines that the resultant calibrated weights do not
provide a unique solution for the executed soft calibration model,
the calibration model validator 138 may determine whether the
executed soft calibration model included a stability parameter. For
example, the calibration model validator 138 of FIG. 1 may
determine that a soft calibration model expressed in a manner
consistent with Equation 17 described above does not include a
stability parameter. If the calibration model validator 138 of FIG.
1 determines that the executed soft calibration model does not
include a stability parameter, the calibration model validator 138
may incorporate a stability parameter into the soft calibration
model, and may further cause the calibration engine 110 of FIG. 1
to re-execute the soft calibration model (e.g., the soft
calibration model including the stability parameter) to
re-determine the calibrated weights. For example, the calibration
model validator 138 of FIG. 1 may incorporate a stability parameter
expressed in a manner consistent with Equation 16 described above
into the soft calibration model expressed in a manner consistent
with Equation 17 described above to provide the soft calibration
model expressed in a manner consistent with Equation 18 described
above (e.g., a soft calibration model including a stability
parameter).
[0076] The example user interface 112 of FIG. 1 facilitates
interactions and/or communications between an end user and the
criteria-based input determiner 102, the unit-based input
determiner 104, the matrix determiner 106, the model parameter
determiner 108, the calibration engine 110, the memory 114, the
calibrated weights determiner 130, the calibrated reporting data
determiner 134, the calibration model validator 138, and/or, more
generally, the calibration apparatus 100 of FIG. 1. The user
interface 112 of FIG. 1 includes one or more input device(s) 140
via which the user may input information and/or data to the
criteria-based input determiner 102, the unit-based input
determiner 104, the matrix determiner 106, the model parameter
determiner 108, the calibration engine 110, the memory 114, the
calibrated weights determiner 130, the calibrated reporting data
determiner 134, the calibration model validator 138, and/or, more
generally, the calibration apparatus 100. For example, the one or
more input device(s) 140 of the user interface 112 may include a
button, a switch, a keyboard, a mouse, a microphone, and/or a
touchscreen that enable(s) the user to convey data and/or commands
to the criteria-based input determiner 102, the unit-based input
determiner 104, the matrix determiner 106, the model parameter
determiner 108, the calibration engine 110, the memory 114, the
calibrated weights determiner 130, the calibrated reporting data
determiner 134, the calibration model validator 138, and/or, more
generally, the calibration apparatus 100 of FIG. 1.
[0077] The user interface 112 of FIG. 1 also includes one or more
output device(s) 142 via which the user interface 112 presents
information and/or data in visual and/or audible form to the user.
For example, the one or more output device(s) 142 of the user
interface 112 may include a light emitting diode, a touchscreen,
and/or a liquid crystal display for presenting visual information,
and/or a speaker for presenting audible information. In some
examples, the one or more output device(s) 142 of the user
interface 112 may present and/or display the example calibrated
weights data 132 and/or the example calibrated panelist and/or
reporting data 136 resulting from execution of the soft calibration
model by the example calibration engine 110 of FIG. 1. In some
examples, the one or more output device(s) 142 of the user
interface 112 may be directed to present and/or display the example
calibrated weights data 132 and/or the example calibrated panelist
and/or reporting data 136 by one or more of the calibration engine
110, the calibrated weights determiner 130, the calibrated
reporting data determiner 134, the calibration model validator 138,
and/or, more generally, the calibration apparatus 100 of FIG. 1.
Data and/or information that is presented and/or received via the
user interface 112 of FIG. 1 may be of any type, form and/or
format, and may be stored in a computer-readable storage medium
such as the example memory 114 of FIG. 1 described below.
[0078] The example memory 114 of FIG. 1 may be implemented by any
type(s) and/or any number(s) of storage device(s) such as a storage
drive, a flash memory, a read-only memory (ROM), a random-access
memory (RAM), a cache and/or any other physical storage medium in
which information is stored for any duration (e.g., for extended
time periods, permanently, brief instances, for temporarily
buffering, and/or for caching of the information). The data and/or
information stored in the memory 114 may be stored in any file
and/or data structure format, organization scheme, and/or
arrangement. The memory 114 is accessible to one or more of the
example criteria-based input determiner 102, the example unit-based
input determiner 104, the example matrix determiner 106, the
example model parameter determiner 108, the example calibration
engine 110, the example user interface 112, the example calibrated
weights determiner 130, the example calibrated reporting data
determiner 134, and/or the example calibration model validator 138
of FIG. 1, and/or, more generally, to the calibration apparatus of
FIG. 1.
[0079] In some examples, the memory 114 of FIG. 1 stores data
and/or information received via the one or more input device(s) 140
of the user interface 112 of FIG. 1. In some examples, the memory
114 stores data and/or information to be presented via the one or
more output device(s) 142 of the user interface 112 of FIG. 1. In
some examples, the memory 114 stores panelist and/or reporting data
116. In some examples, the memory 114 stores criteria-based input
data 118 including criteria associated with the panelist and/or
reporting data 116, criteria variables for the criteria, targets
for the criteria variables, lower bounds for the criteria
variables, upper bounds for the criteria variables, scaling
parameters for the criteria variables, and/or importance parameters
for the criteria variables. In some examples, the memory 114 stores
a target loss function 120 to be incorporated into the soft
calibration model to be executed by the calibration engine 110 of
FIG. 1. In some examples, the memory 114 stores unit-based input
data 122 including units associated with the panelist and/or
reporting data 116, unit variables for the units, initial weights
for the unit variables, lower bounds for the unit variables, upper
bounds for the unit variables, and/or size parameters for the unit
variables. In some examples, the memory 114 stores a weight loss
function 124 to be incorporated into the soft calibration model to
be executed by the calibration engine 110 of FIG. 1. In some
examples, the memory 114 stores matrix data 126. In some examples,
the memory 114 stores model parameter data 128 including a Huber
function parameter, a budget parameter, and/or a stability
parameter. In some examples, the memory 114 stores calibrated
weights data 132 determined and/or calculated by the calibrated
weights determiner 130 and/or, more generally, by the calibration
engine 110 of FIG. 1. In some examples, the memory 114 stores
calibrated panelist and/or reporting data 136 determined and/or
calculated by the calibrated reporting data determiner 134 and/or,
more generally, by the calibration engine 110 of FIG. 1.
[0080] While an example manner of implementing a calibration
apparatus 100 is illustrated in FIG. 1, one or more of the
elements, processes and/or devices illustrated in FIG. 1 may be
combined, divided, re-arranged, omitted, eliminated and/or
implemented in any other way. Further, the example criteria-based
input determiner 102, the example unit-based input determiner 104,
the example matrix determiner 106, the example model parameter
determiner 108, the example calibration engine 110, the example
user interface 112, the example memory 114, the example calibrated
weights determiner 130, the example calibrated reporting data
determiner 134, and/or the example calibration model validator 138
of FIG. 1 may be implemented by hardware, software, firmware and/or
any combination of hardware, software and/or firmware. Thus, for
example, any of the example criteria-based input determiner 102,
the example unit-based input determiner 104, the example matrix
determiner 106, the example model parameter determiner 108, the
example calibration engine 110, the example user interface 112, the
example memory 114, the example calibrated weights determiner 130,
the example calibrated reporting data determiner 134, and/or the
example calibration model validator 138 of FIG. 1 could be
implemented by one or more analog or digital circuit(s), logic
circuits, programmable processor(s), application specific
integrated circuit(s) (ASIC(s)), programmable logic device(s)
(PLD(s)) and/or field programmable logic device(s) (FPLD(s)). When
reading any of the apparatus or system claims of this patent to
cover a purely software and/or firmware implementation, at least
one of the example criteria-based input determiner 102, the example
unit-based input determiner 104, the example matrix determiner 106,
the example model parameter determiner 108, the example calibration
engine 110, the example user interface 112, the example memory 114,
the example calibrated weights determiner 130, the example
calibrated reporting data determiner 134, and/or the example
calibration model validator 138 of FIG. 1 is/are hereby expressly
defined to include a tangible computer-readable storage device or
storage disk such as a memory, a digital versatile disk (DVD), a
compact disk (CD), a Blu-ray disk, etc. storing the software and/or
firmware. Further still, the example calibration apparatus 100 of
FIG. 1 may include one or more elements, processes and/or devices
in addition to, or instead of, those illustrated in FIG. 1, and/or
may include more than one of any or all of the illustrated
elements, processes and devices.
[0081] Flowcharts representative of example machine readable
instructions which may be executed to calibrate data using relaxed
benchmark constraints are shown in FIGS. 2-6. In these examples,
the machine-readable instructions may implement one or more
program(s) for execution by a processor such as the example
processor 702 shown in the example processor platform 700 discussed
below in connection with FIG. 7. The one or more program(s) may be
embodied in software stored on a tangible computer readable storage
medium such as a CD-ROM, a floppy disk, a hard drive, a digital
versatile disk (DVD), a Blu-ray disk, or a memory associated with
the processor 702 of FIG. 7, but the entire program(s) and/or parts
thereof could alternatively be executed by a device other than the
processor 702 of FIG. 7, and/or embodied in firmware or dedicated
hardware. Further, although the example program(s) is/are described
with reference to the flowcharts illustrated in FIGS. 2-6, many
other methods for calibrating data using relaxed benchmark
constrains man alternatively be used. For example, the order of
execution of the blocks may be changed, and/or some of the blocks
described may be changed, eliminated, or combined.
[0082] As mentioned above, the example instructions of FIGS. 2-6
may be stored on a tangible computer readable storage medium such
as a hard disk drive, a flash memory, a read-only memory (ROM), a
compact disk (CD), a digital versatile disk (DVD), a cache, a
random-access memory (RAM) and/or any other storage device or
storage disk in which information is stored for any duration (e.g.,
for extended time periods, permanently, for brief instances, for
temporarily buffering, and/or for caching of the information). As
used herein, the term "tangible computer readable storage medium"
is expressly defined to include any type of computer readable
storage device and/or storage disk and to exclude propagating
signals and to exclude transmission media. As used herein,
"tangible computer readable storage medium" and "tangible machine
readable storage medium" are used interchangeably. Additionally or
alternatively, the example instructions of FIGS. 2-6 may be stored
on a non-transitory computer and/or machine-readable medium such as
a hard disk drive, a flash memory, a read-only memory, a compact
disk, a digital versatile disk, a cache, a random-access memory
and/or any other storage device or storage disk in which
information is stored for any duration (e.g., for extended time
periods, permanently, for brief instances, for temporarily
buffering, and/or for caching of the information). As used herein,
the term "non-transitory computer readable medium" is expressly
defined to include any type of computer readable storage device
and/or storage disk and to exclude propagating signals and to
exclude transmission media. As used herein, when the phrase "at
least" is used as the transition term in a preamble of a claim, it
is open-ended in the same manner as the term "comprising" is open
ended.
[0083] FIG. 2 is a flowchart representative of example machine
readable instructions 200 that may be executed at the example
calibration apparatus 100 of FIG. 1 to calibrate data using relaxed
benchmark constraints. The example program 200 of FIG. 2 may be
implemented to calibrate panelist and/or reporting data using
relaxed benchmark constraints incorporated into a soft calibration
model (e.g., the example soft calibration model of Equation 17 or
the example soft calibration model of Equation 18 described
above).
[0084] The example program 200 of FIG. 2 begins when the example
criteria-based input determiner 102 of FIG. 1 determines
criteria-based input data for a target loss function of the soft
calibration model (block 202). For example, the criteria-based
input determiner 102 of FIG. 1 may determine and/or identify the
example criteria-based input data 118 of FIG. 1 by accessing and/or
obtaining the criteria-based input data 118 from the example memory
114 of FIG. 1, and/or by receiving the criteria-based input data
118 from the example user interface 112 of FIG. 1. In some
examples, the criteria-based input data 118 determined and/or
identified by the criteria-based input determiner 102 of FIG. 1 may
include criteria associated with the example panelist and/or
reporting data 116 of FIG. 1, criteria variables for the criteria,
targets for the criteria variables, lower bounds for the criteria
variables, upper bounds for the criteria variables, scaling
parameters for the criteria variables, and/or importance parameters
for the criteria variables. An example process that may be used to
implement block 202 is further described below in connection with
FIG. 3. Following block 202, control of the example program 200 of
FIG. 2 proceeds to block 204.
[0085] At block 204, the example unit-based input determiner 104 of
FIG. 1 determines unit-based input data for a weight loss function
of the soft calibration model (block 204). For example, the
unit-based input determiner 104 of FIG. 1 may determine and/or
identify the example unit-based input data 122 of FIG. 1 by
accessing and/or obtaining the unit-based input data 122 from the
example memory 114 of FIG. 1, and/or by receiving the unit-based
input data 122 from the example user interface 112 of FIG. 1. In
some examples, the unit-based input data 122 determined and/or
identified by the unit-based input determiner 104 of FIG. 1 may
include units associated with the example panelist and/or reporting
data 116 of FIG. 1, unit variables for the units, initial weights
for the unit variables, lower bounds for the unit variables, upper
bounds for the unit variables, and/or size parameters for the unit
variables. An example process that may be used to implement block
204 is further described below in connection with FIG. 4. Following
block 204, control of the example program 200 of FIG. 2 proceeds to
block 206.
[0086] At block 206, the example matrix determiner 106 of FIG. 1
determines matrix data for the soft calibration model (block 206).
For example, the matrix determiner 106 of FIG. 1 may determine
and/or identify the example matrix data 126 of FIG. 1 by accessing
and/or obtaining the matrix data 126 from the example memory 114 of
FIG. 1, and/or by receiving the matrix data 126 from the example
user interface 112 of FIG. 1. In some examples, the matrix
determiner 106 of FIG. 1 determines and/or identifies the matrix
data 126 based on the example criteria-based input data 118 of FIG.
1 and the example unit-based input data 122 of FIG. 1. In some
examples, the matrix data 126 determined and/or identified by the
matrix determiner 106 of FIG. 1 may be expressed in a manner
consistent with Equation 14 and/or Equation 15 described above.
Following block 206, control of the example program 200 of FIG. 2
proceeds to block 208.
[0087] At block 208, the example model parameter determiner 108 of
FIG. 1 determines model parameter data for the soft calibration
model (block 208). For example, the model parameter determiner 108
of FIG. 1 may determine and/or identify the example model parameter
data 128 of FIG. 1 by accessing and/or obtaining the model
parameter data 128 from the example memory 114 of FIG. 1, and/or by
receiving the model parameter data 128 from the example user
interface 112 of FIG. 1. In some examples, the model parameter data
128 to be determined and/or identified by the model parameter
determiner 108 of FIG. 1 may include a Huber function parameter, a
budget parameter, and/or a stability parameter. An example process
that may be used to implement block 208 is further described below
in connection with FIG. 5. Following block 208, control of the
example program 200 of FIG. 2 proceeds to block 210.
[0088] At block 210, the example calibration engine 110 of FIG. 1
executes the soft calibration model to determine calibrated weights
based on the criteria-based input data, the target loss function,
the unit-based input data, the weight loss function, the design
matrix, and the model parameters (block 210). For example, the
calibration engine 110 of FIG. 1 may execute the soft calibration
model based on the example criteria-based input data 118, the
example target loss function 120, the example unit-based input data
122, the example weight loss function 124, the example matrix data
126, and the example model parameter data 128 of FIG. 1. In
response to the calibration engine 110 of FIG. 1 executing the soft
calibration model, the calibrated weights determiner 130 of FIG. 1
determines the example calibrated weights data 132 of FIG. 1 based
on the criteria-based input data 118, the target loss function 120,
the unit-based input data 122, the weight loss function 124, the
matrix data 126, and the model parameter data 128 incorporated into
the executed soft calibration model. In some examples, the
calibrated weights determiner 130 of FIG. 1 may determine and/or
calculate the calibrated weights data 132 based on adjusted
calibration weights output by the soft calibration model.
[0089] In some examples, the model parameter data 128 incorporated
into the soft calibration model to be executed at block 210
includes a stability parameter. In other examples, the model
parameter data 128 incorporated into the soft calibration model to
be executed at block 210 may lack a stability parameter. An example
process that may be used to implement block 210 when the model
parameter data 128 incorporated into the soft calibration model may
lack a stability parameter is further described below in connection
with FIG. 6. Following block 210, control of the example program
200 of FIG. 2 proceeds to block 212.
[0090] At block 212, the example calibrated reporting data
determiner 134 of FIG. 1 determines calibrated panelist and/or
reporting data based on initial panelist and/or reporting data and
the calibrated weights (block 212). For example, the calibrated
reporting data determiner 134 of FIG. 1 may determine and/or
calculate the example calibrated panelist and/or reporting data 136
of FIG. 1 by applying the example calibrated weights data 132 of
FIG. 1 determined and/or calculated by the calibrated weights
determiner 130 of FIG. 1 to the example panelist and/or reporting
data 116 of FIG. 1. Following block 212, control of the example
program 200 of FIG. 2 proceeds to block 214.
[0091] At block 214, the example user interface 112 of FIG. 1
presents the calibrated weights, and/or presents the calibrated
panelist and/or reporting data, for display (block 214). For
example, the user interface 112 of FIG. 1 may present (e.g.,
display) the example calibrated weights data 132 of FIG. 1
determined and/or calculated by the calibrated weights determiner
130 of FIG. 1. The user interface 112 of FIG. 1 may additionally
and/or alternatively present (e.g., display) the example calibrated
panelist and/or reporting data 136 of FIG. 1 determined and/or
calculated by the calibrated reporting data determiner 134 of FIG.
1. Following block 214, the example program 200 of FIG. 2 ends.
[0092] FIG. 3 is a flowchart representative of example machine
readable instructions 202 that may be executed at the example
calibration apparatus 100 of FIG. 1 to determine criteria-based
input data for the target loss function of the soft calibration
model to be executed by the calibration apparatus 100. Example
operations of blocks 302, 304, 306, 308, 310, 312 and 314 of FIG. 3
may be used to implement block 202 of FIG. 2.
[0093] The example program 202 of FIG. 3 begins when the example
criteria-based input determiner 102 of FIG. 1 determines criteria
associated with panelist and/or reporting data (block 302). For
example, the criteria-based input determiner 102 of FIG. 1 may
determine and/or identify criteria associated the example panelist
and/or reporting data 116 of FIG. 1 by accessing and/or obtaining
the criteria from the example memory 114 of FIG. 1, and/or by
receiving the criteria from the example user interface 112 of FIG.
1. In some examples, the criteria determined and/or identified by
the criteria-based input determiner 102 of FIG. 1 may be expressed
in a manner consistent with Equation 1 described above. Following
block 302, control of the example program 202 of FIG. 3 proceeds to
block 304.
[0094] At block 304, the example criteria-based input determiner
102 of FIG. 1 determines criteria variables for the criteria (block
304). For example, the criteria-based input determiner 102 of FIG.
1 may determine and/or identify criteria variables for the criteria
by accessing and/or obtaining the criteria variables from the
example memory 114 of FIG. 1, and/or by receiving the criteria
variables from the example user interface 112 of FIG. 1. In some
examples, the criteria variables determined and/or identified by
the criteria-based input determiner 102 of FIG. 1 may be expressed
in a manner consistent with Equation 2 described above. Following
block 304, control of the example program 202 of FIG. 3 proceeds to
block 306.
[0095] At block 306, the example criteria-based input determiner
102 of FIG. 1 determines targets for the criteria variables (block
306). For example, the criteria-based input determiner 102 of FIG.
1 may determine and/or identify targets for the criteria variables
by accessing and/or obtaining the targets from the example memory
114 of FIG. 1, and/or by receiving the targets from the example
user interface 112 of FIG. 1. In some examples, the targets
determined and/or identified by the criteria-based input determiner
102 of FIG. 1 may be expressed in a manner consistent with Equation
3 described above. Following block 306, control of the example
program 202 of FIG. 3 proceeds to block 308.
[0096] At block 308, the example criteria-based input determiner
102 of FIG. 1 determines lower bounds for the criteria variables
(block 308). For example, the criteria-based input determiner 102
of FIG. 1 may determine and/or identify lower bounds for the
criteria variables by accessing and/or obtaining the lower bounds
from the example memory 114 of FIG. 1, and/or by receiving the
lower bounds from the example user interface 112 of FIG. 1. In some
examples, the lower bounds determined and/or identified by the
criteria-based input determiner 102 of FIG. 1 may be expressed in a
manner consistent with Equation 4 described above. Following block
308, control of the example program 202 of FIG. 3 proceeds to block
310.
[0097] At block 310, the example criteria-based input determiner
102 of FIG. 1 determines upper bounds for the criteria variables
(block 310). For example, the criteria-based input determiner 102
of FIG. 1 may determine and/or identify upper bounds for the
criteria variables by accessing and/or obtaining the upper bounds
from the example memory 114 of FIG. 1, and/or by receiving the
upper bounds from the example user interface 112 of FIG. 1. In some
examples, the upper bounds determined and/or identified by the
criteria-based input determiner 102 of FIG. 1 may be expressed in a
manner consistent with Equation 4 described above. Following block
310, control of the example program 202 of FIG. 3 proceeds to block
312.
[0098] At block 312, the example criteria-based input determiner
102 of FIG. 1 determines scaling parameters for the criteria
variables (block 312). For example, the criteria-based input
determiner 102 of FIG. 1 may determine and/or identify scaling
parameters for the criteria variables by accessing and/or obtaining
the scaling parameters from the example memory 114 of FIG. 1,
and/or by receiving the scaling parameters from the example user
interface 112 of FIG. 1. In some examples, the scaling parameters
determined and/or identified by the criteria-based input determiner
102 of FIG. 1 may be expressed in a manner consistent with Equation
5 described above. Following block 312, control of the example
program 202 of FIG. 3 proceeds to block 314.
[0099] At block 314, the example criteria-based input determiner
102 of FIG. 1 determines importance parameters for the criteria
variables (block 314). For example, the criteria-based input
determiner 102 of FIG. 1 may determine and/or identify importance
parameters for the criteria variables by accessing and/or obtaining
the importance parameters from the example memory 114 of FIG. 1,
and/or by receiving the importance parameters from the example user
interface 112 of FIG. 1. In some examples, the importance
parameters determined and/or identified by the criteria-based input
determiner 102 of FIG. 1 may be expressed in a manner consistent
with Equation 6 described above. Following block 314, the example
program 202 of FIG. 3 ends and control returns to a calling
function or process such as the example program 200 of FIG. 2.
[0100] FIG. 4 is a flowchart representative of example machine
readable instructions 204 that may be executed at the example
calibration apparatus 100 of FIG. 1 to determine unit-based input
data for the weight loss function of the soft calibration model to
be executed by the calibration apparatus 100. Example operations of
blocks 402, 404, 406, 408, 410 and 412 of FIG. 4 may be used to
implement block 204 of FIG. 2.
[0101] The example program 204 of FIG. 4 begins when the example
unit-based input determiner 104 of FIG. 1 determines units
associated with panelist and/or reporting data (block 402). For
example, the unit-based input determiner 104 of FIG. 1 may
determine and/or identify units associated the example panelist
and/or reporting data 116 of FIG. 1 by accessing and/or obtaining
the units from the example memory 114 of FIG. 1, and/or by
receiving the units from the example user interface 112 of FIG. 1.
In some examples, the units determined and/or identified by the
unit-based input determiner 104 of FIG. 1 may be expressed in a
manner consistent with Equation 8 described above. Following block
402, control of the example program 204 of FIG. 4 proceeds to block
404.
[0102] At block 404, the example unit-based input determiner 104 of
FIG. 1 determines unit variables for the units (block 404). For
example, the unit-based input determiner 104 of FIG. 1 may
determine and/or identify unit variables for the units by accessing
and/or obtaining the unit variables from the example memory 114 of
FIG. 1, and/or by receiving the unit variables from the example
user interface 112 of FIG. 1. In some examples, the unit variables
determined and/or identified by the unit-based input determiner 104
of FIG. 1 may be expressed in a manner consistent with Equation 9
described above. Following block 404, control of the example
program 204 of FIG. 4 proceeds to block 406.
[0103] At block 406, the example unit-based input determiner 104 of
FIG. 1 determines initial weights for the unit variables (block
406). For example, the unit-based input determiner 104 of FIG. 1
may determine and/or identify initial weights for the unit
variables by accessing and/or obtaining the initial weights from
the example memory 114 of FIG. 1, and/or by receiving the initial
weights from the example user interface 112 of FIG. 1. In some
examples, the initial weights determined and/or identified by the
unit-based input determiner 104 of FIG. 1 may be expressed in a
manner consistent with Equation 10 described above. Following block
406, control of the example program 204 of FIG. 4 proceeds to block
408.
[0104] At block 408, the example unit-based input determiner 104 of
FIG. 1 determines lower bounds for the unit variables (block 408).
For example, the unit-based input determiner 104 of FIG. 1 may
determine and/or identify lower bounds for the unit variables by
accessing and/or obtaining the lower bounds from the example memory
114 of FIG. 1, and/or by receiving the lower bounds from the
example user interface 112 of FIG. 1. In some examples, the lower
bounds determined and/or identified by the unit-based input
determiner 104 of FIG. 1 may be expressed in a manner consistent
with Equation 11 described above. Following block 408, control of
the example program 204 of FIG. 4 proceeds to block 410.
[0105] At block 410, the example unit-based input determiner 104 of
FIG. 1 determines upper bounds for the unit variables (block 410).
For example, the unit-based input determiner 104 of FIG. 1 may
determine and/or identify upper bounds for the unit variables by
accessing and/or obtaining the upper bounds from the example memory
114 of FIG. 1, and/or by receiving the upper bounds from the
example user interface 112 of FIG. 1. In some examples, the upper
bounds determined and/or identified by the unit-based input
determiner 104 of FIG. 1 may be expressed in a manner consistent
with Equation 11 described above. Following block 410, control of
the example program 204 of FIG. 4 proceeds to block 412.
[0106] At block 412, the example unit-based input determiner 104 of
FIG. 1 determines size parameters for the unit variables (block
412). For example, the unit-based input determiner 104 of FIG. 1
may determine and/or identify size parameters for the unit
variables by accessing and/or obtaining the size parameters from
the example memory 114 of FIG. 1, and/or by receiving the size
parameters from the example user interface 112 of FIG. 1. In some
examples, the size parameters determined and/or identified by the
unit-based input determiner 104 of FIG. 1 may be expressed in a
manner consistent with Equation 12 described above. Following block
412, the example program 204 of FIG. 4 ends and control returns to
a calling function or process such as the example program 200 of
FIG. 2.
[0107] FIG. 5 is a flowchart representative of example machine
readable instructions 208 that may be executed at the example
calibration apparatus 100 of FIG. 1 to determine model parameters
for the soft calibration model to be executed by the calibration
apparatus 100. Example operations of blocks 502, 504 and 506 of
FIG. 5 may be used to implement block 208 of FIG. 2.
[0108] The example program 208 of FIG. 5 begins when the example
model parameter determiner 108 of FIG. 1 determines a Huber
function parameter for the soft calibration model (block 502). For
example, the model parameter determiner 108 of FIG. 1 may determine
and/or identify a Huber function parameter for the soft calibration
model by accessing and/or obtaining the Huber function parameter
from the example memory 114 of FIG. 1, and/or by receiving the
Huber function parameter from the example user interface 112 of
FIG. 1. Following block 502, control of the example program 208 of
FIG. 5 proceeds to block 504.
[0109] At block 504, the example model parameter determiner 108 of
FIG. 1 determines a budget parameter for the soft calibration model
(block 504). For example, the model parameter determiner 108 of
FIG. 1 may determine and/or identify a budget parameter for the
soft calibration model by accessing and/or obtaining the budget
parameter from the example memory 114 of FIG. 1, and/or by
receiving the budget parameter from the example user interface 112
of FIG. 1. Following block 504, control of the example program 208
of FIG. 5 proceeds to block 506.
[0110] At block 506, the example model parameter determiner 108 of
FIG. 1 determines a stability parameter for the soft calibration
model (block 506). For example, the model parameter determiner 108
of FIG. 1 may determine and/or identify a stability parameter for
the soft calibration model by accessing and/or obtaining the
stability parameter from the example memory 114 of FIG. 1, and/or
by receiving the stability parameter from the example user
interface 112 of FIG. 1. Following block 506, the example program
208 of FIG. 5 ends and control returns to a calling function or
process such as the example program 200 of FIG. 2.
[0111] FIG. 6 is a flowchart representative of example machine
readable instructions 210 that may be executed at the example
calibration apparatus 100 of FIG. 1 to validate the soft
calibration model executed by the calibration apparatus. Example
operations of blocks 602, 604, 606, 608, 610, 612, 614 and 616 of
FIG. 6 may be used to implement block 210 of FIG. 2 in instances
when the model parameter data 128 incorporated into the soft
calibration model may lack a stability parameter.
[0112] The example program 210 of FIG. 6 begins when the example
calibration model validator 138 of FIG. 1 determines whether the
soft calibration model executed by the example calibration engine
110 of FIG. 1 includes a stability parameter (block 602). For
example, the calibration model validator 138 of FIG. 1 may
determine that a soft calibration model expressed in a manner
consistent with Equation 17 described above does not include a
stability parameter. If the calibration model validator 138
determines at block 602 that the soft calibration model executed by
the calibration engine 110 of FIG. 1 does not include a stability
parameter, control of the example program 210 of FIG. 6 proceeds to
block 604. If the calibration model validator 138 instead
determines at block 602 that the soft calibration model executed by
the calibration engine 110 of FIG. 1 does include a stability
parameter, the example program 210 of FIG. 6 ends and control
returns to a calling function or process such as the example
program 200 of FIG. 2.
[0113] At block 604, the example calibration model validator 138 of
FIG. 1 determines whether the calibrated weights resulting from the
soft calibration model being executed by the example calibration
engine 110 of FIG. 1 provide a unique solution for the executed
soft calibration model (block 604). If the calibration model
validator 138 determines at block 604 that the calibrated weights
resulting from the soft calibration model being executed by the
example calibration engine 110 of FIG. 1 do not provide a unique
solution for the executed soft calibration model, control of the
example program 210 of FIG. 6 proceeds to block 606. If the
calibration model validator 138 instead determines at block 604
that the calibrated weights resulting from the soft calibration
model being executed by the example calibration engine 110 of FIG.
1 do provide a unique solution for the executed soft calibration
model, the example program 210 of FIG. 6 ends and control returns
to a calling function or process such as the example program 200 of
FIG. 2.
[0114] At block 606, the example calibration model validator 138 of
FIG. 1 incorporates a stability parameter into the soft calibration
model (block 606). For example, the calibration model validator 138
of FIG. 1 may incorporate a stability parameter expressed in a
manner consistent with Equation 16 described above into the soft
calibration model expressed in a manner consistent with Equation 17
described above to provide the soft calibration model expressed in
a manner consistent with Equation 18 described above (e.g., a soft
calibration model including a stability parameter). Following block
606, control of the example program 210 of FIG. 6 proceeds to block
608.
[0115] At block 608, the example calibration engine 110 of FIG. 1
re-executes the soft calibration model to re-determine the
calibrated weights (block 608). For example, the calibration engine
110 of FIG. 1 may re-execute the soft calibration model based on
the example criteria-based input data 118, the example target loss
function 120, the example unit-based input data 122, the example
weight loss function 124, the example matrix data 126, and the
example model parameter data 128 of FIG. 1, including the stability
parameter. In response to the calibration engine 110 of FIG. 1
executing the soft calibration model, the calibrated weights
determiner 130 of FIG. 1 determines the example calibrated weights
data 132 of FIG. 1 based on the criteria-based input data 118, the
target loss function 120, the unit-based input data 122, the weight
loss function 124, the matrix data 126, and the model parameter
data 128 incorporated into the executed soft calibration model,
including the stability parameter. The calibrated weights
determined (e.g., re-determined) at block 608 provide a unique
solution for the re-executed soft calibration model. Following
block 608, the example program 210 of FIG. 6 ends and control
returns to a calling function or process such as the example
program 200 of FIG. 2.
[0116] FIG. 7 is an example processor platform 700 capable of
executing the instructions of FIGS. 2-6 to implement the example
calibration apparatus 100 of FIG. 1. The processor platform 700 of
the illustrated example includes a processor 702. The processor 702
of the illustrated example is hardware. For example, the processor
702 can be implemented by one or more integrated circuit(s), logic
circuit(s), controller(s), microcontroller(s) and/or
microprocessor(s) from any desired family or manufacturer. The
processor 702 of the illustrated example includes a local memory
704 (e.g., a cache). The processor 702 of the illustrated example
also includes the example criteria-based input determiner 102, the
example unit-based input determiner 104, the example matrix
determiner 106, the example model parameter determiner 108, the
example calibration engine 110, the example calibrated weights
determiner 130, the example calibrated reporting data determiner
134, and the example calibration model validator 138 of FIG. 1.
[0117] The processor 702 of the illustrated example is also in
communication with a main memory including a volatile memory 706
and a non-volatile memory 708 via a bus 710. The volatile memory
706 may be implemented by Synchronous Dynamic Random Access Memory
(SDRAM), Dynamic Random Access Memory (DRAM), RAMBUS Dynamic Random
Access Memory (RDRAM) and/or any other type of random access memory
device. The non-volatile memory 708 may be implemented by flash
memory and/or any other desired type of memory device. Access to
the volatile memory 706 and the non-volatile memory 708 is
controlled by a memory controller.
[0118] The processor 702 of the illustrated example is also in
communication with one or more mass storage device(s) 712 for
storing software and/or data. Examples of such mass storage devices
712 include floppy disk drives, hard disk drives, compact disk
drives, Blu-ray disk drives, RAID systems, and digital versatile
disk (DVD) drives. In the illustrated example of FIG. 7, the mass
storage device 712 includes the example memory 114 of FIG. 1.
[0119] The processor platform 700 of the illustrated example also
includes a user interface circuit 714. The user interface circuit
714 may be implemented by any type of interface standard, such as
an Ethernet interface, a universal serial bus (USB), and/or a PCI
express interface. In the illustrated example, one or more input
device(s) 140 are connected to the user interface circuit 714. The
input device(s) 140 permit(s) a user to enter data and commands
into the processor 702. The input device(s) 140 can be implemented
by, for example, an audio sensor, a camera (still or video), a
keyboard, a button, a mouse, a touchscreen, a track-pad, a
trackball, isopoint, a voice recognition system, a microphone,
and/or a liquid crystal display. One or more output device(s) 142
are also connected to the user interface circuit 714 of the
illustrated example. The output device(s) 142 can be implemented,
for example, by a light emitting diode, an organic light emitting
diode, a liquid crystal display, a touchscreen and/or a speaker.
The user interface circuit 714 of the illustrated example may,
thus, include a graphics driver such as a graphics driver chip
and/or processor. In the illustrated example, the input device(s)
140, the output device(s) 142 and the user interface circuit 714
collectively form the example user interface 112 of FIG. 1.
[0120] The processor platform 700 of the illustrated example also
includes a network interface circuit 716. The network interface
circuit 716 may be implemented by any type of interface standard,
such as an Ethernet interface, a universal serial bus (USB), and/or
a PCI express interface. In the illustrated example, the network
interface circuit 716 facilitates the exchange of data and/or
signals with external machines (e.g., a remote server) via a
network 718 (e.g., a local area network (LAN), a wireless local
area network (WLAN), a wide area network (WAN), the Internet, a
cellular network, etc.).
[0121] Coded instructions 720 corresponding to FIGS. 2-6 may be
stored in the local memory 704, in the volatile memory 706, in the
non-volatile memory 708, in the mass storage device 712, and/or on
a removable tangible computer readable storage medium such as a
flash memory stick, a CD or DVD.
[0122] From the foregoing, it will be appreciated that methods,
systems and apparatus have been disclosed for calibrating data
(e.g., panelist and/or reporting data) using relaxed benchmark
constraints. Unlike hard calibration models and/or techniques
requiring that estimated totals associated with projection weights
match reference and/or benchmark totals precisely, the disclosed
soft calibration models and/or techniques advantageously generate
adjusted and/or modified projection weights such that the distance
and/or deviation between the estimated totals and the reference
and/or benchmark totals is smaller than some particular value
(e.g., a threshold and/or budget). By relaxing the benchmark
constraints associated with traditional hard calibration models
and/or techniques, the disclosed soft calibration models and/or
techniques advantageously reduce (e.g., eliminate) the
above-described errors that may arise in connection with the use of
hard calibration models and/or techniques when the calibration
weights take on a relatively large magnitude. Thus, a data
measurement company implementing the disclosed soft calibration
models and/or techniques in lieu of traditional hard calibration
models and/or techniques may advantageously provide and/or generate
calibrated panelist and/or reporting data that more closely matches
and/or resembles reference and/or benchmark data.
[0123] Apparatus for generating a unique solution when calibrating
data via a calibration model having relaxed benchmark constraints
are disclosed. In some disclosed examples, the apparatus comprises
a calibration engine to execute the calibration model based on a
target loss function, a weight loss function, and a budget
parameter. In some disclosed examples, the apparatus further
comprises a calibrated weights determiner to determine calibrated
weights resulting from execution of the calibration model. In some
disclosed examples, the apparatus further comprises a calibration
model validator to incorporate a stability parameter into the
calibration model in response to determining that the calibrated
weights do not provide a unique solution for the executed
calibration model. In some disclosed examples, the stability
parameter is to reduce an influence of the budget parameter on the
calibration model to enable the generation of a unique
solution.
[0124] In some disclosed examples, the calibration engine is to
re-execute the calibration model based on the target loss function,
the weight loss function, the budget parameter, and the stability
parameter. In some disclosed examples, the calibrated weights
determiner is to re-determine the calibrated weights resulting from
re-execution of the calibration model. In some disclosed examples,
the re-determined calibrated weights are to provide a unique
solution for the re-executed calibration model.
[0125] In some disclosed examples, the calibration engine is to
execute the calibration model based further on criteria-based input
data to be incorporated into the target loss function and
unit-based input data to be incorporated into the weight loss
function. In some disclosed examples, the criteria-based input data
includes criteria variables, targets for the criteria variables,
upper and lower bounds for the criteria variables, scaling
parameters for the criteria variables, and importance parameters
for the criteria variables. In some disclosed examples, the
unit-based input data includes unit variables, initial weights for
the unit variables, upper and lower bounds for the unit variables,
and size parameters for the unit variable. In some disclosed
examples, the calibration engine is to execute the calibration
model based further on matrix data. In some disclosed examples, the
matrix data is based on the criteria-based input data and the
unit-based input data.
[0126] Methods for generating a unique solution when calibrating
data via a calibration model having relaxed benchmark constraints
are disclosed. In some disclosed examples, the method comprises
executing the calibration model based on a target loss function, a
weight loss function, and a budget parameter. In some disclosed
examples, the method further comprises determining, by executing
one or more computer readable instructions with a processor,
calibrated weights resulting from the executing of the calibration
model. In some disclosed examples, the method further comprises
incorporating, by executing one or more computer readable
instructions with the processor, a stability parameter into the
calibration model in response to determining that the calibrated
weights do not provide a unique solution for the executed
calibration model. In some disclosed examples, the stability
parameter is to reduce an influence of the budget parameter on the
calibration model to enable the generation of a unique
solution.
[0127] In some disclosed examples, the method further includes
re-executing the calibration model based on the target loss
function, the weight loss function, the budget parameter, and the
stability parameter. In some disclosed examples, the method further
includes re-determining the calibrated weights resulting from the
re-executing of the calibration model. In some disclosed examples,
the re-determined calibrated weights are to provide a unique
solution for the re-executed calibration model.
[0128] In some disclosed examples, the executing of the calibration
model is further based on criteria-based input data incorporated
into the target loss function and unit-based input data
incorporated into the weight loss function. In some disclosed
examples, the criteria-based input data includes criteria
variables, targets for the criteria variables, upper and lower
bounds for the criteria variables, scaling parameters for the
criteria variables, and importance parameters for the criteria
variables. In some disclosed examples, the unit-based input data
includes unit variables, initial weights for the unit variables,
upper and lower bounds for the unit variables, and size parameters
for the unit variables. In some disclosed examples, the executing
of the calibration model is further based on matrix data. In some
disclosed examples, the matrix data is based on the criteria-based
input data and the unit-based input data.
[0129] Tangible machine-readable storage media comprising
instructions are also disclosed. In some disclosed examples, the
instructions, when executed, cause a processor to execute a
calibration model based on a target loss function, a weight loss
function, and a budget parameter. In some disclosed examples, the
calibration model has relaxed benchmark constraints. In some
disclosed examples, the instructions, when executed, cause the
processor to determine calibrated weights resulting from the
execution of the calibration model. In some disclosed examples, the
instructions, when executed, cause the processor to incorporate a
stability parameter into the calibration model in response to
determining that the calibrated weights do not provide a unique
solution for the executed calibration model. In some disclosed
examples, the stability parameter is to reduce an influence of the
budget parameter on the calibration model to enable the generation
of a unique solution.
[0130] In some disclosed examples, the instructions, when executed,
are further to cause the processor to re-execute the calibration
model based on the target loss function, the weight loss function,
the budget parameter, and the stability parameter. In some
disclosed examples, the instructions, when executed, are further to
cause the processor to re-determine the calibrated weights
resulting from the re-execution of the calibration model. In some
disclosed examples, the re-determined calibrated weights are to
provide a unique solution for the re-executed calibration
model.
[0131] In some disclosed examples, the instructions, when executed,
are to cause the processor to execute the calibration model based
further on criteria-based input data incorporated into the target
loss function and unit-based input data incorporated into the
weight loss function. In some disclosed examples, the
criteria-based input data includes criteria variables, targets for
the criteria variables, upper and lower bounds for the criteria
variables, scaling parameters for the criteria variables, and
importance parameters for the criteria variables. In some disclosed
examples, the unit-based input data includes unit variables,
initial weights for the unit variables, upper and lower bounds for
the unit variables, and size parameters for the unit variables. In
some disclosed examples, the instructions, when executed, are to
cause the processor to execute the calibration model based further
on matrix data. In some disclosed examples, the matrix data is
based on the criteria-based input data and the unit-based input
data.
[0132] Although certain example methods, apparatus and articles of
manufacture have been disclosed herein, the scope of coverage of
this patent is not limited thereto. On the contrary, this patent
covers all methods, apparatus and articles of manufacture fairly
falling within the scope of the claims of this patent.
* * * * *