Deep Gaussian Processes with Importance-Weighted Variational Inference

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.

Appearing ICML 2019

Cited by in corpus (8)

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• A Tutorial on Sparse Gaussian Processes and Variational Inference
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• Compositional Modeling of Nonlinear Dynamical Systems with ODE-based Random Features
• Conditional Deep Gaussian Processes: multi-fidelity kernel learning
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• Modulating Scalable Gaussian Processes for Expressive Statistical Learning