Gradient-based explanations for Gaussian Process regression and classification models

Gaussian Processes (GPs) have proven themselves as a reliable and effective method in probabilistic Machine Learning. Thanks to recent and current advances, modeling complex data with GPs is becoming more and more feasible. Thus, these types of models are, nowadays, an interesting alternative to Neural and Deep Learning methods, which are arguably the current state-of-the-art in Machine Learning. For the latter, we see an increasing interest in so-called explainable approaches - in essence methods that aim to make a Machine Learning model's decision process transparent to humans. Such methods are particularly needed when illogical or biased reasoning can lead to actual disadvantageous consequences for humans. Ideally, explainable Machine Learning should help detect such flaws in a model and aid a subsequent debugging process. One active line of research in Machine Learning explainability are gradient-based methods, which have been successfully applied to complex neural networks. Given that GPs are closed under differentiation, gradient-based explainability for GPs appears as a promising field of research. This paper is primarily focused on explaining GP classifiers via gradients where, contrary to GP regression, derivative GPs are not straightforward to obtain.