Modulating Scalable Gaussian Processes for Expressive Statistical Learning

TL;DR

This paper introduces scalable Gaussian process models with latent variables and variational inference techniques to better capture complex, non-Gaussian data distributions in large datasets, outperforming existing methods.

Contribution

It proposes new scalable GP paradigms, including non-stationary heteroscedastic, mixture, and latent GPs, with tailored variational inference strategies for improved modeling of complex data.

Findings

Scalable latent GP outperforms state-of-the-art models on diverse tasks.

New variational inference methods enable efficient training of complex GPs.

The proposed models effectively learn heteroscedastic, multi-modal, and non-stationary data distributions.

Abstract

For a learning task, Gaussian process (GP) is interested in learning the statistical relationship between inputs and outputs, since it offers not only the prediction mean but also the associated variability. The vanilla GP however struggles to learn complicated distribution with the property of, e.g., heteroscedastic noise, multi-modality and non-stationarity, from massive data due to the Gaussian marginal and the cubic complexity. To this end, this article studies new scalable GP paradigms including the non-stationary heteroscedastic GP, the mixture of GPs and the latent GP, which introduce additional latent variables to modulate the outputs or inputs in order to learn richer, non-Gaussian statistical representation. We further resort to different variational inference strategies to arrive at analytical or tighter evidence lower bounds (ELBOs) of the marginal likelihood for efficient and effective model training. Extensive numerical experiments against state-of-the-art GP and neural network (NN) counterparts on various tasks verify the superiority of these scalable modulated GPs, especially the scalable latent GP, for learning diverse data distributions.