The Variational Gaussian Process

Dustin Tran; Rajesh Ranganath; David M. Blei

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arXiv · 1511.06499

The Variational Gaussian Process

Dustin Tran·Rajesh Ranganath·David M. Blei

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Abstract

Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric variational family, which adapts its shape to match complex posterior distributions. The VGP generates approximate posterior samples by generating latent inputs and warping them through random non-linear mappings; the distribution over random mappings is learned during inference, enabling the transformed outputs to adapt to varying complexity. We prove a universal approximation theorem for the VGP, demonstrating its representative power for learning any model. For inference we present a variational objective inspired by auto-encoders and perform black box inference over a wide class of models. The VGP achieves new state-of-the-art results for unsupervised learning, inferring models such as the deep latent Gaussian model and the recently proposed DRAW.

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BibTeX RIS

Dustin Tran, Rajesh Ranganath, David M. Blei. 2016-04-17. The Variational Gaussian Process. https://arxiv.org/abs/1511.06499

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