We propose a new forecasting procedure that includes randomized hierarchical dynamic regression models with random parameters, measurement noises and random input. We developed the technology of entropy-randomized machine learning, which includes the estimation of characteristics of a dynamic regression model and its testing by generating ensembles of predicted trajectories through the sampling of the entropy-optimal probability density functions of the model parameters and measurement noises. The density functions are determined at the learning stage by solving the constrained maximization problem of an information entropy functional subject to the empirical balances with real data. The proposed procedure is applied to the randomized forecasting of the daily electrical load in a regional power system. We construct a two-layer dynamic model of the daily electrical load. One of the layers describes the dependence of electrical load on ambient temperature while the other simulates the stochastic quasi-fluctuating temperature dynamics.

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Abstract:We propose a new method of randomized forecasting (RF-method), which operates with models described by systems of linear ordinary differential equations with random parameters. The RF-method is based on entropy-robust estimation of the probability density functions (PDFs) of model parameters and measurement noises. The entropy-optimal estimator uses a limited amount of data. The method of randomized forecasting is applied to World population prediction. Ensembles of entropy-optimal prognostic trajectories of World population and their probability characteristics are generated. We show potential preferences of the proposed method in comparison with existing methods.