ABSTRACT
In this chapter, we present four important topics that we have not discussed in the previous chapters, and raise some open issues regarding them that are worth further consideration. Section 8.1 discusses a Gaussian process regression model with multivariate response variables. For a multivariate GPR model the difficulty is in defining a cross-variance function. We discuss a method for constructing a cross-variance function based on convolution (Boyle and Frean, 2005). In Section 8.2, we discuss a GP latent variable model that models the nonlinear relationships between observed functionalmanifest variables and unobserved functional latent variables by a GPR model. Section 8.3 discusses how to use a GPR model to find the optimal dynamic control in a nonlinear system. Section 8.4 tries to explain the relationship between the GPR model and RKHS (reproducing kernel Hilbert space). The current research on most of these topics up to the time of writing this book is limited and worthy of further development. In this regard, we briefly introduce some basic ideas and the theory of these topics in this chapter. We indeed hope readers, both those who are experienced as well as newcomers to the area, add their insights to the research.
