Deep Gaussian Processes with Importance-Weighted Variational Inference

TL;DR

This paper introduces a novel importance-weighted variational inference method for deep Gaussian processes, improving accuracy over classical methods, especially in deeper models, by incorporating noisy variables as latent covariates.

Contribution

It proposes a new importance-weighted objective for DGPs that leverages analytic results and balances computation and accuracy, outperforming previous variational approaches.

Findings

Importance-weighted objective improves inference accuracy.

Method outperforms classical variational inference in deep models.

Incorporating noisy variables as latent covariates enhances modeling of complex data.

Abstract

Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables to the model. Previous work on DGP models has introduced noise additively and used variational inference with a combination of sparse Gaussian processes and mean-field Gaussians for the approximate posterior. Additive noise attenuates the signal, and the Gaussian form of variational distribution may lead to an inaccurate posterior. We instead incorporate noisy variables as latent covariates, and propose a novel importance-weighted objective, which leverages analytic results and provides a mechanism to trade off computation for improved accuracy. Our results demonstrate that the importance-weighted objective works well in practice and consistently outperforms classical variational inference, especially for deeper models.