Parameter-dependent model-blending with multi-expert based machine learning and proxy sites

1. A multi-expert based machine learning method to determine a blended forecasting model, the method comprising:

running a set of individual models to identify critical parameters, wherein the critical parameters are determined to be critical to estimation of a parameter of interest, wherein the identifying the critical parameters includes examining first order dependence and second order dependence of an error in the estimation of the parameter of interest associated with each of the parameters estimated by each of the set of individual models and wherein examining the first order dependence includes translating a first order error dependence curve into two coefficients and examining the second order dependence includes translating a second order error dependence surface into six coefficients, wherein each individual model from the set of individual models is associated with a particular site of a set of sites and wherein each site from the set of sites has a corresponding latitude, longitude, and elevation;

storing historical data, the historical data including estimates and measurements of the parameter of interest and estimates of the critical parameters;

obtaining training data as the historical data with a particular combination of values of the critical parameters;

correlating a type associated with each site with the latitude, the longitude, and the elevation of the site by training a plurality of machine learning models, which are different than any of the set of individual models, with respective machine learning algorithms using the training data that includes a first set of parameter values associated with a first range of time points, the first set of parameter values being obtained from the historical data, wherein the training the plurality of the machine learning models with the machine learning algorithms includes training the plurality of the machine learning models to correlate the site type with the latitude, the longitude, and the elevation of the site;

obtaining estimates of the parameter of interest with each of the machine learning models using the training data that includes a second set of parameter values associated with a second range of time points, the second set of parameter values being obtained from the historical data;

determining, using a processor, a most accurate machine learning model among the machine learning models at each time point in the second range of time points; and

determining the blended forecasting model based on the most accurate machine learning model determined for each time point in the second range of time points by training a classification machine learning model to correlate, for each time point in the second range of time points, the most accurate machine learning model with corresponding values of the critical parameters in the historical data and inputting the corresponding values of the critical parameters into the trained classification machine learning model, wherein the blended forecasting model corresponding with critical parameters is determined as the most accurate machine learning model correlated with the critical parameters.

2. The method according to claim 1 , wherein each of the machine learning algorithms blends the set of individual models.

3. The method according to claim 2 , further comprising obtaining estimates of the critical parameters from the set of individual models to determine the blended forecasting model.

4. The method according to claim 1 , wherein the training the plurality of the machine learning models with the machine learning algorithms includes training with a linear regression, random forest regression, gradient boosting regression tree, support vector machine, or neural network.

5. The method according to claim 1 , wherein the determining the most accurate machine learning model at each time point in the second range of time points includes comparing the respective estimate of the parameter of interest obtained with each of the machine learning models at the associated time point with a corresponding measurement of the parameter of interest in the historical data.

6. The method according to claim 1 , wherein the determining the blended forecasting model includes selecting one of the machine learning models determined as the most accurate machine learning model as the blended forecasting model.

7. A multi-expert based machine learning system to determine a blended forecasting model, the system comprising:

a memory device to store historical data of parameters, the historical data including estimates and measurements of a parameter of interest and estimates of critical parameters determined to be critical to an estimate of the parameter of interest, wherein the critical parameters are identified based on running a set of individual models, wherein the critical parameters are identified by examining first order dependence and second order dependence of an error in the estimation of the parameter of interest associated with each of the parameters estimated by each of the set of individual models and wherein examining the first order dependence includes translating a first order error dependence curve into two coefficients and examining the second order dependence includes translating a second order error dependence surface into six coefficients, wherein each individual model from the set of individual models is associated with a particular site of a set of sites and wherein each site from the set of sites has a corresponding latitude, longitude, and elevation; and

a processor configured to obtain training data as the historical data with a particular combination of values of the critical parameter, to correlate a type associated with each site with the latitude, the longitude, and the elevation of the site by training a plurality of learning models, which are different than any of the set of individual models, with respective machine learning algorithms using the training data that includes a first set of parameter values associated with a first range of time points obtained from the historical data, wherein the training the plurality of the machine learning models with the machine learning algorithms includes training the plurality of the machine learning models to correlate the site type with the latitude, the longitude, and the elevation of the site, to obtain estimates of the parameter of interest with each of the machine learning models using the training data that includes a second set of parameter values associated with a second range of time points, the second set of parameter values being obtained from the historical data, to determine a most accurate machine learning model among the machine learning models at each time point in the second range of time points, and to determine the blended forecasting model from the most accurate machine learning models by training a classification machine learning model to correlate, for each time point in the second range of time points, the most accurate machine learning model with corresponding values of the critical parameters in the historical data and inputting the corresponding values of the critical parameters into the trained classification machine learning model, wherein the blended forecasting model corresponding with critical parameters is determined as the most accurate machine learning model correlated with the critical parameters.

8. The system according to claim 7 , wherein each of the machine learning algorithms blends the set of individual models.

9. The system according to claim 8 , wherein the set of individual models estimates the critical parameters.

10. The system according to claim 7 , wherein the machine learning algorithms include training with a linear regression, random forest regression, gradient boosting regression tree, support vector machine, or neural network.

11. The system according to claim 7 , wherein the processor compares the respective estimate of the parameter of interest obtained with each of the machine learning models at the associated time point in the second range of time points with a corresponding measurement of the parameter of interest in the historical data to determine the most accurate machine learning model at each time point in the range of time points.

12. A non-transitory computer program product having computer readable instructions stored thereon which, when executed by a processor, cause the processor to implement a method of determining a blended forecasting model, the method comprising:

obtaining historical data, the historical data including estimates and measurements of a parameter of interest and estimates of critical parameters, the critical parameters determined to be critical to an estimate of the parameter of interest, wherein the critical parameters are identified based on running a set of individual models, wherein the critical parameters are identified by examining first order dependence and second order dependence of an error in the estimation of the parameter of interest associated with each of the parameters estimated by each of the set of individual models and wherein examining the first order dependence includes translating a first order error dependence curve into two coefficients and examining the second order dependence includes translating a second order error dependence surface into six coefficients, wherein each individual model from the set of individual models is associated with a particular site of a set of sites and wherein each site from the set of sites has a corresponding latitude, longitude, and elevation;

obtaining training data as the historical data with a particular combination of values of the critical parameters;

correlating a type associated with each site with the latitude, the longitude, and the elevation of the site by training a plurality of machine learning models, which are different than any of the set of individual models, with respective machine learning algorithms using the training data that includes a first set of parameter values associated with a first range of time points, the first set of parameter values being obtained from the historical data, wherein the training the plurality of the machine learning models with the machine learning algorithms includes training the plurality of the machine learning models to correlate the site type with the latitude, the longitude, and the elevation of the site;

obtaining estimates of the parameter of interest with each of the machine learning models using the training data that includes a second set of parameter associated with a second range of time points, the second set of parameter values being obtained from the historical data;

determining a most accurate machine learning model among the machine learning models at each time point in the second range of time points; and

determining the blended forecasting model based on the most accurate machine learning model determined for each time point in the second range of time points by training a classification machine learning model to correlate, for each time point in the second range of time points, the most accurate machine learning model with corresponding values of the critical parameters in the historical data and inputting the corresponding values of the critical parameters into the trained classification machine learning model, wherein the blended forecasting model corresponding with critical parameters is determined as the most accurate machine learning model correlated with the critical parameters.

13. The non-transitory computer program product according to claim 12 , wherein each of the machine learning algorithms blends the set of individual models.

14. The non-transitory computer program product according to claim 13 , further comprising obtaining estimates of the critical parameters from the set of individual models to determine the blended forecasting model.

15. The non-transitory computer program product according to claim 12 , wherein the training the plurality of the machine learning models with the machine learning algorithms includes training with a linear regression, random forest regression, gradient boosting regression tree, support vector machine, or neural network.

16. The non-transitory computer program product according to claim 12 , wherein the determining the most accurate machine learning model at each time point in the second range of time points includes comparing the respective estimate of the parameter of interest obtained with each of the machine learning models at the associated time point with a corresponding measurement of the parameter of interest in the historical data.