Adaptive selection of the optimal order of linear regression models using learning automata

This paper concerns the adaptive selection of the optimal order of linear regression models using a variable-structure stochastic learning automaton. The Alaike criterion is derived for stationary and non-stationary cases, and it is shown that the optimal order minimizes a loss function corresponding to the evaluation of this criterion. The order of the regression model belongs to a finite set. Each order value is associated with an action of the automaton. The Bush-Mosteller reinforcement scheme with normalized automaton input is used to adjust the probability distribution. Simulation results illustrate the feasibility and performance of this model order selection approach