Control system with machine learning time-series modeling

1. A control system to control devices based on an unsupervised machine learning modeling, the control system comprising:

an artificial intelligence server including at least one processor;

a data storage system to store historic time-series data for independent variables and a dependent variable, and a time series forecasting model; and

an unsupervised machine learning modeling system including machine readable instructions stored on a non-transitory computer readable medium and executed by the artificial intelligence server to:

build the time series forecasting model from the stored historic time-series data according to an unsupervised machine learning function, wherein the time series forecasting model includes the independent variables from the stored historic time-series data and the dependent variable from the stored historic time-series data, and wherein the building of the time series forecasting model comprises:

determining a time-varying parameter (β) for each of the independent variables and for continuous consecutive time intervals of the stored historic time-series data;

restricting a variance of at least one of the β's if overfitting for the time series forecasting model is estimated to occur; and

for each of the independent variables, multiplying the independent variable with the time-varying parameter for the independent variable; and

apply the time series forecasting model to a data set, wherein the applying of the time series forecasting model includes:

determining whether the time series forecasting model is to be applied for making predictions for higher granularity time intervals that are larger than the time intervals of the stored time-series data used to build the model;

if the predictions are for the higher granularity time intervals, modifying the β's for the independent variables to be for higher granularity time intervals;

estimating a contribution of each of the independent variables for each of the consecutive time periods to the dependent variable; and

controlling at least one device according to the estimated contributions of the independent variables.

2. The control system of claim 1 , wherein restricting a variance of at least one of the β's comprises:

restricting the variance of at least one of the β's based on a variation between actual values and predicted values of the dependent variable.

3. The control system of claim 2 , wherein restricting the variance of at least one of the β's based on a variation between actual values and predicted values of the dependent variable comprises:

determining an actual values Relative Standard Deviation (RSD) of actual values of the dependent variable;

determining a 95% confidence interval for the RSD of actual values of the dependent variable;

determining a predicted values RSD of predicted values of the dependent variable;

determining whether the predicted values RSD is within the 95% confidence interval;

if the predicted values RSD is not within the 95% confidence interval, modifying at least one of the β's for the independent variable for the time series forecasting model if a level of variance between the predicted values RSD and the 95% confidence interval exceeds a threshold; and

if the predicted values RSD of the dependent variable is within the 95% confidence interval, the β's for the independent variables are not modified.

4. The control system of claim 3 , wherein modifying at least one of the β's comprises:

through an iterative process, restricting the β's for the independent variables by a predetermined percentage until the predicted values RSD is within the 95% confidence interval or the level of variance between the predicted values RSD and the 95% confidence is less than or equal to the threshold.

5. The control system of claim 1 , wherein modifying the β's to be for higher granularity time intervals comprises:

determining a best likelihood estimate, a best case estimate, and worst case estimate for each of the β's for the higher granularity time intervals; and

determining a probability for each of the best likelihood estimates, the best case estimates, and the worst case estimates; and

using one of the best likelihood estimates, the best case estimates, and the worst case estimates of the β's as the modified β's.

6. The control system of claim 1 , wherein modifying the β's to be for higher granularity time intervals comprises:

determining a probability distribution of the β's;

using Ordinary Least Squares (OLS) to determine the best likelihood estimates;

calculating the predicted values for the β's; and

using the predicted values to compute the best case estimates and the worst case estimates.

7. A non-transitory computer readable medium comprising machine readable instructions executable by at least one processor to:

determine an unsupervised machine learning function;

build a time series forecasting model from historic time-series data according to the unsupervised machine learning function, wherein the time series forecasting model includes independent variables from the stored historic time-series data and a dependent variable from the stored historic time-series data, and wherein to build the time series forecasting model, the at least one processor is to:

determine a time-varying parameter (β) for each of the independent variables and for continuous consecutive time intervals of the historic time-series data;

restrict a variance of at least one of the β's if overfitting for the time series forecasting model is estimated to occur; and

for each of the independent variables, multiply the independent variable with the time-varying parameter for the independent variable; and

apply the time series forecasting model to a data set, wherein the applying of the time series forecasting model includes:

estimating a contribution of each of the independent variables for each of the consecutive time periods to the dependent variable; and

controlling at least one device according to the estimated contributions of the independent variables.

8. The non-transitory computer readable medium of claim 7 , wherein the machine readable instructions executable by the at least one processor to restrict a variance of at least one of the β's are further to:

restrict the variance of at least one of the β's based on a variation between actual values and predicted values of the dependent variable.

9. The non-transitory computer readable medium of claim 8 , wherein the machine readable instructions executable by the at least one processor to restrict the variance of at least one of the β's based on a variation between actual values and predicted values of the dependent variable comprises are further to:

for each independent variable:

determine an actual values Relative Standard Deviation (RSD) of actual values of the dependent variable;

determine a 95% confidence interval for the RSD of actual values of the dependent variable;

determining a predicted values RSD of predicted values of the dependent variable;

determine whether the predicted values RSD is within the 95% confidence interval;

if the predicted values RSD is not within the 95% confidence interval, modify at least one of the β's for the independent variable for the time series forecasting model if a level of variance between the predicted values RSD and the 95% confidence interval exceeds a threshold; and

if the predicted values RSD of the dependent variable is within the 95% confidence interval, the β's for the independent variables are not modified.

10. The non-transitory computer readable medium of claim 9 , wherein the machine readable instructions executable by the at least one processor to modify at least one of the β's are to:

through an iterative process, restrict the β's for the independent variables by a predetermined percentage until the predicted values RSD is within the 95% confidence interval or the level of variance between the predicted values RSD and the 95% confidence is less than or equal to the threshold.

11. The non-transitory computer readable medium of claim 7 , wherein the machine readable instructions executable by the at least one processor to apply the time series forecasting model are to:

determine whether the time series forecasting model is to be applied for making predictions for higher granularity time intervals that are larger than the time intervals of the stored time-series data used to build the model;

if the predictions are for the higher granularity time intervals, modify the β's for the independent variables to be for higher granularity time intervals.

12. The non-transitory computer readable medium of claim 11 , wherein the machine readable instructions executable by the at least one processor to modify the β's to be for higher granularity time intervals are to:

determine a best likelihood estimate, a best case estimate, and worst case estimate for each of the β's for the higher granularity time intervals; and

determine a probability for each of the best likelihood estimates, the best case estimates, and the worst case estimates; and

use one of the best likelihood estimates, the best case estimates, and the worst case estimates of the β's as the modified β's.

13. A non-transitory computer readable medium comprising machine readable instructions executable by at least one processor to:

determine an unsupervised machine learning function; and

build a time series forecasting model from historic time-series data according to the unsupervised machine learning function, wherein the time series forecasting model includes independent variables from the stored historic time-series data and a dependent variable from the stored historic time-series data, and wherein to build the time series forecasting model, the at least one processor is to:

determine a time-varying parameter (β) for each of the independent variables and for continuous consecutive time intervals of the historic time-series data;

restrict a variance of at least one of the β's if overfitting for the time series forecasting model is estimated to occur; and

for each of the independent variables, multiply the independent variable with the time-varying parameter for the independent variable; and

apply the time series forecasting model to a data set, wherein to apply the time series forecasting model the at least one processor is to:

estimate a contribution of each of the independent variables for each of the consecutive time periods to the dependent variable;

determine whether the time series forecasting model is to be applied for making predictions for higher granularity time intervals that are larger than the time intervals of the stored time-series data used to build the model;

if the predictions are for the higher granularity time intervals, modify the β's for the independent variables to be for higher granularity time intervals; and

control at least one device according to the estimated contributions of the independent variables.

14. The non-transitory computer readable medium of claim 13 , wherein the machine readable instructions executable by the at least one processor to restrict a variance of at least one of the β's are to:

restrict the variance of at least one of the β's based on a variation between actual values and predicted values of the dependent variable.

15. The non-transitory computer readable medium of claim 14 , wherein the machine readable instructions executable by the at least one processor to restrict the variance of at least one of the β's based on a variation between actual values and predicted values of the dependent variable are to:

determine an actual values Relative Standard Deviation (RSD) of actual values of the dependent variable;

determine a 95% confidence interval for the RSD of actual values of the dependent variable;

determine a predicted values RSD of predicted values of the dependent variable;

determine whether the predicted values RSD is within the 95% confidence interval;

if the predicted values RSD is not within the 95% confidence interval, modifying at least one of the β's for the independent variable for the time series forecasting model if a level of variance between the predicted values RSD and the 95% confidence interval exceeds a threshold; and

if the predicted values RSD of the dependent variable is within the 95% confidence interval, the β's for the independent variables are not modified.

16. The non-transitory computer readable medium of claim 15 , wherein the machine readable instructions executable by the at least one processor to modify at least one of the β's are to:

through an iterative process, restrict the β's for the independent variables by a predetermined percentage until the predicted values RSD is within the 95% confidence interval or the level of variance between the predicted values RSD and the 95% confidence is less than or equal to the threshold.

17. The non-transitory computer readable medium of claim 13 , wherein the machine readable instructions executable by the at least one processor to modify the β's to be for higher granularity time intervals are to:

determine a best likelihood estimate, a best case estimate, and worst case estimate for each of the β's for the higher granularity time intervals; and

determine a probability for each of the best likelihood estimates, the best case estimates, and the worst case estimates; and

use one of the best likelihood estimates, the best case estimates, and the worst case estimates of the β's as the modified β's.

18. The non-transitory computer readable medium of claim 13 , wherein the machine readable instructions executable by the at least one processor to modify the β's to be for higher granularity time intervals are to:

determine a probability distribution of the β's;

use Ordinary Least Squares (OLS) to determine the best likelihood estimates;

calculate the predicted values for the β's; and

use the predicted values to compute the best case estimates and the worst case estimates.