Semiparametric Regression Using Student $t$ Processes

In this paper, we propose a latent factor regression model, in which priors are assigned to both the latent regression vector and the error term, by using reproducing kernels. The resulting regression function follows a stochastic process known as a student process. The model is attractive because its implementation is based on a tractable posterior predictive distribution and a simple expectation-maximization (EM) estimation algorithm. In addition, treating the transductive inference as a missing data problem, we devise the EM algorithm to deal with the parameter estimation as well as the response prediction in a single paradigm. The model is also elaborated for multivariate-response regression problems. For this purpose, we present a generalization of multivariate models and some of its properties. Experimental results show our approaches to be effective.