Covariance Kernel Learning Schemes for Gaussian Process Based Prediction Using Markov Chain Monte Carlo

Probabilistic supervised learning within the Bayesian paradigm typically use Gaussian Processes (GPs) to model the sought function, and provide a means for securing reliable uncertainties in said functional learning, while offering interpretability. Prediction of the output of such a learnt function is closed-form in this approach. In this work, we present GP based learning of the functional relation between two variables, using various kinds of kernels that are called in to parametrise the covariance function of the invoked GP. However, such covariance kernels are typically parametric in the literature, with hyperparameters that are learnt from the data. Here, we discuss a new nonparametric covariance kernel, and compare its performance against existing non-stationary and stationary kernels, as well as against Deep Neural Networks. We present results on both univariate and multivariate data, to demonstrate the range of applicability of the presented learning scheme.