Average Mean Functions Based EM Algorithm for Mixtures of Gaussian Processes

Tao Li, Xiao Luo, Jinwen Ma

Abstract: The mixture of Gaussian process functional regressions (mix-GPFR) utilizes a linear combination of certain B-spline functions to fit the mean functions of Gaussian processes. Although mix-GPFR makes the mean functions active in the mixture of Gaussian processes, there are two limitations: (1). This linear combination approximation introduces many parameters and thus a heavy cost of computation is paid for learning these mean functions. (2). It is implicitly assumed that the mean functions of different components share the same degree of smoothness because there is a parameter controlling the smoothness globally. In order to get rid of these limitations, we propose a new kind of EM algorithm for mixtures of Gaussian processes with average mean functions from time-aligned batch trajectory or temporal data. In this way, the mean functions are iteratively updated according to the distributed trajectory data of the estimated Gaussian processes at each iteration of the EM algorithm and the effectiveness of this estimation is also theoretically analyzed. It is demonstrated by the experimental results on both synthetic and real-world datasets that the proposed method performs well.