报告题目：A Two-layer Mixture Model of Gaussian Process Functional Regressions
The mixture of Gaussian processes is capable of learning any general stochastic process based on a given set of (sample) curves for the regression and prediction problems. However, it is ineffective for curve clustering and prediction when the sample curves are derived from different stochastic processes as independent sources linearly mixed together. In this paper, we propose a two-layer mixture model of Gaussian Process Functional Regressions (GPFRs) to describe such a mixture of general stochastic processes or independent sources, especially for curve clustering and prediction. Specifically, in the lower layer, the Mixture of GPFRs (MGPFR) is developed for a cluster (or class) of curves within the input space. In the higher layer, the mixture of MGPFRs is further established to divide the curves into clusters according to its components in the output space. For the parameter estimation of the two-layer mixture of GPFRs, we develop a Monte Carlo EM algorithm based on a Monte Carlo Markov Chain (MCMC) method, in short, the MCMC EM algorithm. We validate the hierarchical mixture of GPFRs and MCMC EM algorithm using synthetic and real-world datasets. Our results show that our new model outperforms the conventional mixture models in curve clustering and prediction.