STRIDE: Sparse Techniques for Regression in Deep Gaussian Processes

• URL: http://arxiv.org/abs/2505.11355v1
• Date: Fri, 16 May 2025 15:18:15 GMT
• Title: STRIDE: Sparse Techniques for Regression in Deep Gaussian Processes
• Authors: Simon Urbainczyk, Aretha L. Teckentrup, Jonas Latz,
• Abstract summary: We develop a particle-based expectation expectation training method for deep GP training on large-scale data.<n>We test our method on standard benchmark problems.
• Score: 0.3277163122167433
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is large or when the underlying function contains multi-scale features that are difficult to represent by a stationary kernel. To address the former, training of GPs with large-scale data is often performed through inducing point approximations (also known as sparse GP regression (GPR)), where the size of the covariance matrices in GPR is reduced considerably through a greedy search on the data set. To aid the latter, deep GPs have gained traction as hierarchical models that resolve multi-scale features by combining multiple GPs. Posterior inference in deep GPs requires a sampling or, more usual, a variational approximation. Variational approximations lead to large-scale stochastic, non-convex optimisation problems and the resulting approximation tends to represent uncertainty incorrectly. In this work, we combine variational learning with MCMC to develop a particle-based expectation-maximisation method to simultaneously find inducing points within the large-scale data (variationally) and accurately train the GPs (sampling-based). The result is a highly efficient and accurate methodology for deep GP training on large-scale data. We test our method on standard benchmark problems.

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