Unbiased Stochastic Optimization for Gaussian Processes on Finite Dimensional RKHS

2025-08-28

AI Summary

Existing Gaussian process (GP) methods for stochastic hyperparameter learning suffer from biased gradients or rely on inducing-point approximations, hindering convergence to stationary points of the true marginal likelihood. This paper proposes an unbiased stochastic inference framework grounded in finite-dimensional reproducing kernel Hilbert spaces (RKHS). It is the first to yield unbiased stochastic gradient estimates of the marginal likelihood—without inducing points or variational approximations—thereby guaranteeing convergence to stationary points of the exact objective. Theoretically, the approach extends to infinite-dimensional RKHS and remains robust under resource constraints. Experiments demonstrate that, in memory-limited settings—such as small mini-batches or few inducing points—the method significantly outperforms baselines including stochastic variational inference, achieving superior model fit and predictive performance.

Technology Category

• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Current methods for stochastic hyperparameter learning in Gaussian Processes (GPs) rely on approximations, such as computing biased stochastic gradients or using inducing points in stochastic variational inference. However, when using such methods we are not guaranteed to converge to a stationary point of the true marginal likelihood. In this work, we propose algorithms for exact stochastic inference of GPs with kernels that induce a Reproducing Kernel Hilbert Space (RKHS) of moderate finite dimension. Our approach can also be extended to infinite dimensional RKHSs at the cost of forgoing exactness. Both for finite and infinite dimensional RKHSs, our method achieves better experimental results than existing methods when memory resources limit the feasible batch size and the possible number of inducing points.

Problem

• Exact stochastic inference for Gaussian Processes
• Overcoming biased approximations in hyperparameter learning
• Addressing memory constraints in batch and inducing points

Innovation

• Exact stochastic inference for finite dimensional RKHS
• Extendable to infinite dimensional RKHS with approximations
• Better performance under memory constraints than existing methods