Accelerated Continuous Conditional Random Fields For Load Forecasting

Increasingly, aiming to contain their rapidly growing energy expenditures, commercial buildings are equipped to respond to utility's demand and price signals. Such smart energy consumption, however, heavily relies on accurate short-term energy load forecasting, such as hourly predictions for the next n (n ≥ 2) hours. To attain sufficient accuracy for these predictions, it is important to exploit the relationships among the n estimated outputs. This paper treats such multi-steps ahead regression task as a sequence labeling (regression) problem, and adopts the continuous conditional random fields (CCRF) to explicitly model these interconnected outputs. In particular, we improve the CCRF's computation complexity and predictive accuracy with two novel strategies. First, we employ two tridiagonal matrix computation techniques to significantly speed up the CCRF's training and inference. These techniques tackle the cubic computational cost required by the matrix inversion calculations in the training and inference of the CCRF, resulting in linear complexity for these matrix operations. Second, we address the CCRF's weak feature constraint problem with a novel multi-target edge function, thus boosting the CCRF's predictive performance. The proposed multi-target feature is able to convert the relationship of related outputs with continuous values into a set of “sub-relationships”, each providing more specific feature constraints for the interplays of the related outputs. We applied the proposed approach to two real-world energy load prediction systems: one for electricity demand and another for gas usage. Our experimental results show that the proposed strategy can meaningfully reduce the predictive error for the two systems, in terms of mean absolute percentage error and root mean square error, when compared with three benchmarking methods. Promisingly, the relative error reduction achieved by our CCRF model was up to 50 percent.