Bayesian Ying-Yang system and theory as a unified statistical learning approach: (V) - Temporal modeling for perception and control

This paper (1) systematically presents Bayesian Ying-Yang Temporal Modeling (BYY-TM) theory for perception and control in an environments that changes with time. Not only some special cases of BYY-TM are shown to reduce into (a) the conventional State Space Modeling (SSM) with Kalman filtering algorithm, (b) the well known Hidden Markov Model (HMM) and (c) Recurrent Neural Nets (RNN), but also a number of new results are obtained according to this BYY-TM theory. First, new extensions of the Kalman filtering algorithm have been obtained for the cases of nongaussian noise and nonlinear SSM model. Second, the SSM has been extended into models for temporal factor analysis, temporal independent component analysis acid temporal dependence reduction, with algorithms for parameter learning and criteria for deciding the number of factors or sources. Third, a fast adaptive algorithm is proposed for HMM learning and a criterion is given for determining the number of states. Fourth, a criterion has been obtained for selecting the number of hidden recurrent units in three layer recurrent net.