Beyond Gaussian Likelihood: A Review of Generalized Gaussian Processes

The Hong Kong University of Science and Technology (Guangzhou)

Data Science and Analytics Thrust

PhD Qualifying Examination

By Ms LU, Xiaohan

Abstract

Gaussian processes (GPs) constitute a fundamental tool in Bayesian nonparametric modeling, offering closed-form inference under Gaussian likelihoods and benefiting from strong theoretical guarantees. However, this conjugacy assumption restricts their applicability to a limited range of data types. To overcome these constraints, generalized Gaussian processes (GGPs) have been developed, extending GPs to settings with non-Gaussian likelihoods. This survey traces the evolution of GGP methodologies, from early approximation-based techniques to recent advances in scalable and flexible inference. Rather than merely cataloging existing methods, we synthesize these developments into a unified framework that emphasizes the core statistical–computational trade-offs arising from the loss of conjugacy. We examine how these trade-offs emerge across different inference strategies, interact with structural and scalability extensions, and contribute to persistent challenges in practical applications. Finally, we contend that future progress in GGP research hinges on unified inference frameworks that can systematically reconcile flexibility, accuracy, and computational efficiency

PQE Committee

Chair of Committee: Prof. WANG, Xin

Prime Supervisor: Prof. WANG, Wenjia

Co-Supervisor: Prof. ZHONG, Zixin

Examiner: Prof. LI, Lei