Variational Learning of Gaussian Process Latent Variable Models through Stochastic Gradient Annealed Importance Sampling

TL;DR

This paper introduces an Annealed Importance Sampling approach for Gaussian Process Latent Variable Models, improving posterior exploration and variational bounds in high-dimensional and complex data scenarios.

Contribution

It proposes a novel AIS-based method that enhances the analysis of GPLVMs by better exploring the posterior distribution and reparameterizing variables for efficiency.

Findings

Outperforms state-of-the-art methods in variational bounds

Achieves higher log-likelihoods on datasets

Demonstrates robust convergence in experiments

Abstract

Gaussian Process Latent Variable Models (GPLVMs) have become increasingly popular for unsupervised tasks such as dimensionality reduction and missing data recovery due to their flexibility and non-linear nature. An importance-weighted version of the Bayesian GPLVMs has been proposed to obtain a tighter variational bound. However, this version of the approach is primarily limited to analyzing simple data structures, as the generation of an effective proposal distribution can become quite challenging in high-dimensional spaces or with complex data sets. In this work, we propose an Annealed Importance Sampling (AIS) approach to address these issues. By transforming the posterior into a sequence of intermediate distributions using annealing, we combine the strengths of Sequential Monte Carlo samplers and VI to explore a wider range of posterior distributions and gradually approach the target distribution. We further propose an efficient algorithm by reparameterizing all variables in the evidence lower bound (ELBO). Experimental results on both toy and image datasets demonstrate that our method outperforms state-of-the-art methods in terms of tighter variational bounds, higher log-likelihoods, and more robust convergence.