Sparse Variational Inference for Generalized GP Models
Rishit Sheth, Yuyang Wang, Roni Khardon
Abstract
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.
BibTeX
@InProceedings{pmlr-v37-sheth15,
title = {Sparse Variational Inference for Generalized GP Models},
author = {Sheth, Rishit and Wang, Yuyang and Khardon, Roni},
booktitle = {Proceedings of the 32nd International Conference on Machine Learning},
pages = {1302--1311},
year = {2015},
editor = {Bach, Francis and Blei, David},
volume = {37},
series = {Proceedings of Machine Learning Research},
address = {Lille, France},
month = {07--09 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v37/sheth15.pdf},
url = {https://proceedings.mlr.press/v37/sheth15.html},
abstract = {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.}
}