A Markov Chain Monte Carlo approach for Pseudo-Input selection in Sparse Gaussian Processes

The effectiveness of non-parametric methods for regression comes at the price of high computational complexity. In fact, these methods scale as O(N-3), where N is the number of available data points. One possible option to address this issue consists in introducing a set of fictitious (pseudo-) inputs of size M N such that the computational effort is reduced to O((MN)-N-2). To estimate hyper-parameters and pseudo-inputs, a non-convex optimization problem needs to be solved. As opposed to the conventional gradient-based approach used in the literature, this paper proposes a stochastic scheme leveraging Markov Chain Monte Carlo methods. Numerical comparisons show that the latter returns a more efficient set of pseudo-inputs, leading to a superior performance in terms of mean squared error.Copyright (c) 2023 The Authors.