Sparse Variational Inference for Generalized GP Models

author: Rishit Sheth, Department of Computer Science, Tufts University
published: Sept. 27, 2015,   recorded: July 2015,   views: 1590

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Gaussian processes (GP) provide an attractive machine learning model due to their non-parametric form, their flexibility to capture many types of observation data, and their generic inference procedures. Sparse GP inference algorithms address the cubic complexity of GPs by focusing on a small set of pseudo-samples. To date, such approaches have focused on the simple case of Gaussian observation likelihoods. This paper develops a variational sparse solution for GPs under general likelihoods by providing a new characterization of the gradients required for inference in terms of individual observation likelihood terms. In addition, we propose a simple new approach for optimizing the sparse variational approximation using a fixed point computation. We demonstrate experimentally that the fixed point operator acts as a contraction in many cases and therefore leads to fast convergence. An experimental evaluation for count regression, classification, and ordinal regression illustrates the generality and advantages of the new approach.

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