Temporal BYY learning for state space approach, hidden Markov model, and blind source separation

The temporal Bayesian Yang-Yang (TBYY) learning has been presented for signal modeling in a general state space approach, which provides not only a unified point of view on the Kalman filter, hidden Markov model (HMM), independent component analysis (ICA), and blind source separation (BSS) with extensions, but also further advances on these studies, including a higher order HMM, independent HMM for binary BSS, temporal ICA (TICA), and temporal factor analysis for real BSS without and with noise. Adaptive algorithms are developed for implementation and criteria are provided for selecting an appropriate number of states or sources. Moreover, theorems are given on the conditions for source separation by linear and nonlinear TICA. Particularly, it has been shown that not only non-Gaussian but also Gaussian sources can also be separated by TICA via exploring temporal dependence. Experiments are also demonstrated.