BRIEF: Bayesian Regression of Infinite Expert Forecasters for single and multiple time series prediction

Bayesian Regression of Infinite Expert Forecasters (BRIEF) as proposed in the study is a prediction algorithm for time-varying systems. The method is based on regret minimization by tracking the performance of an inifinite pool of experts for single and multiple time series. The inverse correlation weighted error (ICWE) employed in BRIEF takes into account the dependency structure among multiple time series, which can also be adapted to multi-step ahead predictions. Theoretical bounds show that the cumulative regret grows at rate O(log T) with respect to the oracle that can select the best strategy in retrospect. As the per round regret vanishes, BRIEF is indistinguishable to the oracle when the horizon increases. Also since the bound applies to any choice of input subject to the euclidean norm constraint, the method can be applied to adversarial settings. Experimental results verify that BRIEF excels in single and multiple steps ahead prediction of ARMAX simulated data and building energy consumptions.