Self-Distillation for Gaussian Process Regression and Classification

Kenneth Borup; Lars Nørvang Andersen

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arXiv · 2304.02641

Self-Distillation for Gaussian Process Regression and Classification

Kenneth Borup·Lars Nørvang Andersen

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Abstract

We propose two approaches to extend the notion of knowledge distillation to Gaussian Process Regression (GPR) and Gaussian Process Classification (GPC); data-centric and distribution-centric. The data-centric approach resembles most current distillation techniques for machine learning, and refits a model on deterministic predictions from the teacher, while the distribution-centric approach, re-uses the full probabilistic posterior for the next iteration. By analyzing the properties of these approaches, we show that the data-centric approach for GPR closely relates to known results for self-distillation of kernel ridge regression and that the distribution-centric approach for GPR corresponds to ordinary GPR with a very particular choice of hyperparameters. Furthermore, we demonstrate that the distribution-centric approach for GPC approximately corresponds to data duplication and a particular scaling of the covariance and that the data-centric approach for GPC requires redefining the model from a Binomial likelihood to a continuous Bernoulli likelihood to be well-specified. To the best of our knowledge, our proposed approaches are the first to formulate knowledge distillation specifically for Gaussian Process models.

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Kenneth Borup, Lars Nørvang Andersen. 2023-04-05. Self-Distillation for Gaussian Process Regression and Classification. https://arxiv.org/abs/2304.02641

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