Methods, systems and apparatus for calibrating data using relaxed benchmark constraints

1. An apparatus for generating a unique solution when calibrating data via a calibration model having relaxed benchmark constraints, the apparatus comprising:

a calibration engine to execute the calibration model based on a target loss function, a weight loss function, and a budget parameter, the budget parameter being an upper constraint that a weight loss value determined via the weight loss function is allowed to obtain;

a calibrated weights determiner to determine calibrated weights resulting from execution of the calibration model; and

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, 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 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, and the calibrated weights determiner is to re-determine the calibrated weights resulting from re-execution of the calibration model.

3. The apparatus as defined in claim 2 , wherein the re-determined calibrated weights are to provide a unique solution for the re-executed calibration model.

4. The apparatus as defined in claim 1 , wherein 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.

5. The apparatus as defined in claim 4 , wherein the criteria-based input data includes criteria variables and 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.

6. The apparatus as defined in claim 4 , wherein the unit-based input data includes unit variables and 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.

7. The apparatus as defined in claim 4 , wherein the calibration engine is to execute the calibration model based further on matrix data, the matrix data being based on the criteria-based input data and the unit-based input data.

8. A method for generating a unique solution when calibrating data via a calibration model having relaxed benchmark constraints, the method comprising:

executing the calibration model based on a target loss function, a weight loss function, and a budget parameter, the budget parameter being an upper constraint that a weight loss value determined via the weight loss function is allowed to obtain;

determining, by executing one or more computer readable instructions with a 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.

9. The method as defined in claim 8 , further including:

re-executing the calibration model based on 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.

10. The method as defined in claim 9 , wherein the re-determined calibrated weights are to provide a unique solution for the re-executed calibration model.

11. The method as defined in claim 8 , wherein 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.

12. The method as defined in claim 11 , wherein the criteria-based input data includes criteria variables and 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.

13. The method as defined in claim 11 , wherein the unit-based input data includes unit variables and 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.

14. The method as defined in claim 11 , wherein the executing of the calibration model is further based on matrix data, the matrix data being based on the criteria-based input data and the unit-based input data.

15. A tangible machine-readable storage medium comprising instructions that, when executed, cause a processor to at least:

execute a calibration model based on a target loss function, a weight loss function, and a budget parameter, the calibration model having relaxed benchmark constraints, the budget parameter being an upper constraint that a weight loss value determined via the weight loss function is allowed to obtain;

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.

16. The tangible machine-readable storage medium as defined in claim 15 , wherein 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; and

re-determine the calibrated weights resulting from the re-execution of the calibration model.

17. The tangible machine-readable storage medium as defined in claim 16 , wherein the re-determined calibrated weights are to provide a unique solution for the re-executed calibration model.

18. The tangible machine-readable storage medium as defined in claim 15 , wherein 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.

19. The tangible machine-readable storage medium as defined in claim 18 , wherein the criteria-based input data includes criteria variables and 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.

20. The tangible machine-readable storage medium as defined in claim 18 , wherein the unit-based input data includes unit variables and 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.

21. The apparatus as defined in claim 1 , wherein the target loss function has a flat region, the stability parameter to prevent a minimization procedure of the calibration model from reaching the flat region.