DP-GP-LVM: A Bayesian Non-Parametric Model for Learning Multivariate Dependency Structures

TL;DR

This paper introduces a Bayesian non-parametric model that learns complex dependency structures in multivariate data using Gaussian processes and Dirichlet processes, improving upon previous models with a novel inference method.

Contribution

The paper proposes a flexible Bayesian latent variable model combining Gaussian process priors with Dirichlet process priors to learn dependency structures, addressing limitations of earlier models.

Findings

Effective learning of dependency structures across dimensions

Improved inference efficiency through variational bounds

Circumvents issues of previous Gaussian process latent variable models

Abstract

We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and interchangeable Dirichlet process priors to learn the structure. The introduction of the Dirichlet process as a specific structural prior allows our model to circumvent issues associated with previous Gaussian process latent variable models. Inference is performed by deriving an efficient variational bound on the marginal log-likelihood on the model.