An Analysis of Posterior Collapse, Parameterization and Initialization in Variational Deep Gaussian Processes

2026-06-24

AI Summary

This work addresses the issue of posterior collapse in variational deep Gaussian processes (DGPs), which often causes the model to degenerate into a noise explainer. The authors systematically analyze the root causes and demonstrate that the empirical benefits of linear prior mean functions stem not from mitigating non-injective pathologies, but rather from improved optimization initialization. Building on this insight, they propose a novel initialization strategy for zero-mean priors that effectively prevents collapse without requiring structural constraints. The study further provides the first theoretical explanation for how whitened parameterizations enhance convergence stability. Experimental results show that the proposed method significantly improves training stability and achieves performance on par with or superior to conventional DGP models employing linear prior mean functions across multiple tasks.

Abstract

DGPs are probabilistic models with remarkable prediction performance that concatenate GPs across several layers. Exact inference in DGPs is intractable, and variational inference is often used to approximate the posterior with a parametric distribution tuned by minimizing the Kullback-Leibler divergence. Moreover, finding a good VI approximation is challenging. In particular, a problem of VI is posterior collapse, where VI converges to a variational posterior that matches the prior. In variational DGPs, this implies explaining the data as noise. This work studies posterior collapse in DGPs and identifies its connection to the DSVI algorithm and the widely used linear prior mean function employed in all but the last layer. We show that the benefit of the linear prior mean does not arise from avoiding the non-injective pathology in very deep DGPs, as previously believed, but from improving the conditioning of the optimization problem at initialization. Thus, we propose an alternative initialization of a zero prior mean DGP that mimics a DGP with a linear prior mean at initialization. This enables successful training of DGPs without imposing optimization-driven constraints on the prior, allowing to choose the prior based on modeling assumptions rather than optimization convenience. Our analysis considers three common parameterizations of DGPs and shows that not all of them benefit from a linear prior mean. We also explain why a whitened parameterization of the \DGP provides more stable convergence, something often assumed from experience, but lacking a rigorous analysis. Furthermore, we show that this stability is also beneficial to avoid the posterior collapse problem. Extensive experiments validate our findings: the proposed initialization prevents posterior collapse, improves stability, and achieves performance comparable to (and sometimes better than) DGPs with a linear prior mean.

Problem

• posterior collapse
• variational inference
• deep Gaussian processes
• parameterization
• initialization

Innovation

• posterior collapse
• deep Gaussian processes
• variational inference
• initialization
• whitened parameterization