Sarem Seitz

Sarem Seitz

Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an interesting alternative to deep learning and related approaches. As the latter are getting more and more influential on society, the need for making a model's decision making process transparent and explainable is now a major focus of research. A major direction in interpretable machine learning is the use of gradient-based approaches, such as Integrated Gradients, to quantify feature attribution, locally for a given datapoint of interest. Since GPs and the behavior of their partial derivatives are well studied and straightforward to derive, studying gradient-based explainability for GPs is a promising direction of research. Unfortunately, partial derivatives for GPs become less trivial to handle when dealing with non-Gaussian target data as in classification or more sophisticated regression problems. This paper therefore proposes an approach for applying Integrated Gradient-based explainability to non-Gaussian GP models, offering both analytical and approximate solutions. This extends gradient-based explainability to probabilistic models with complex likelihoods to extend their practical applicability.

Sarem Seitz

Gaussian Processes (GPs) are a versatile and popular method in Bayesian Machine Learning. A common modification are Sparse Variational Gaussian Processes (SVGPs) which are well suited to deal with large datasets. While GPs allow to elegantly deal with Gaussian-distributed target variables in closed form, their applicability can be extended to non-Gaussian data as well. These extensions are usually impossible to treat in closed form and hence require approximate solutions. This paper proposes to approximate the inverse-link function, which is necessary when working with non-Gaussian likelihoods, by a piece-wise constant function. It will be shown that this yields a closed form solution for the corresponding SVGP lower bound. In addition, it is demonstrated how the piece-wise constant function itself can be optimized, resulting in an inverse-link function that can be learnt from the data at hand.

Sarem Seitz

Bayesian methods have become a popular way to incorporate prior knowledge and a notion of uncertainty into machine learning models. At the same time, the complexity of modern machine learning makes it challenging to comprehend a model's reasoning process, let alone express specific prior assumptions in a rigorous manner. While primarily interested in the former issue, recent developments intransparent machine learning could also broaden the range of prior information that we can provide to complex Bayesian models. Inspired by the idea of self-explaining models, we introduce a corresponding concept for variational GaussianProcesses. On the one hand, our contribution improves transparency for these types of models. More importantly though, our proposed self-explaining variational posterior distribution allows to incorporate both general prior knowledge about a target function as a whole and prior knowledge about the contribution of individual features.

Sarem Seitz

When constructing a Bayesian Machine Learning model, we might be faced with multiple different prior distributions and thus are required to properly consider them in a sensible manner in our model. While this situation is reasonably well explored for classical Bayesian Statistics, it appears useful to develop a corresponding method for complex Machine Learning problems. Given their underlying Bayesian framework and their widespread popularity, Gaussian Processes are a good candidate to tackle this task. We therefore extend the idea of Mixture models for Gaussian Process regression in order to work with multiple prior beliefs at once - both a analytical regression formula and a Sparse Variational approach are considered. In addition, we consider the usage of our approach to additionally account for the problem of prior misspecification in functional regression problems.