Non-central Student-t Mixture of Student-t Processes for Robust Regression and Prediction

Abstract

The Mixture of Gaussian Processes (MGP) is a general regression model for the data from a general stochastic process. However, there are two drawbacks on the parameter learning of the MGP model. First, it is sensitive to outliers. Actually, when the data are disturbed by heavy noise, its regression results are affected greatly by the noise, which makes it difficult to reflect the overall characteristics of the data. Second, the kernels of Gaussian processes in the MGP model do not have a simple parametric form to represent uncertain intuition by nonparametric prior over the covariance matrix. In order to overcome these problems, we propose the non-central student-t Mixture of student-t Processes (tMtP) model for robust regression and prediction. Specifically, the student-t process takes the invers Wishart distribution as its conjugate prior for the covariance matrix. The learning of the mixture parameters in the tMtP model can be implemented under the general framework of the hard-cut EM algorithm while the learning of the hyperparameters in each student-t process is implemented by maximizing the log-likelihood function of the square exponential kernel in output region. It is demonstrated by the experimental results on synthetic data sets that the tMtP model is effective for robust regression. Moreover, the tMtP model also obtains good prediction performance on a coal production data set.