Uncovering the Interpretability and Identifiability of Gaussian Processes: From Application to Theory

Gaussian processes (GPs) are widely employed as versatile modeling and predictive tools in spatial statistics, functional data analysis, computer modeling and diverse applications of machine learning. While GPs are commonly used for prediction, in certain applications, the focus is on parameter inference. To illustrate the importance of parameter inference, we will examine a specific application of Gaussian processes in enhancer-promoter time series. We will then delve into the existing literature on the identifiability theory of Gaussian process parameters in the Euclidean domain, and discuss extensions to the compact Riemannian manifold domain. Our talk aims to provide insights into the interpretability and applicability of Gaussian processes beyond their traditional use in prediction tasks.

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