Heterogeneous Multi-output Gaussian Process Prediction

TL;DR

This paper introduces a novel multi-output Gaussian process model capable of handling heterogeneous outputs with different likelihoods, using a joint latent function framework and variational inference for scalable prediction.

Contribution

It extends Gaussian processes to model multiple heterogeneous outputs with distinct likelihoods using a vector-valued prior and a linear coregionalisation covariance structure.

Findings

Effective on synthetic data

Performs well on real datasets

Scalable variational inference implementation

Abstract

We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in all likelihoods as latent functions. Our multi-output Gaussian process uses a covariance function with a linear model of coregionalisation form. Assuming conditional independence across the underlying latent functions together with an inducing variable framework, we are able to obtain tractable variational bounds amenable to stochastic variational inference. We illustrate the performance of the model on synthetic data and two real datasets: a human behavioral study and a demographic high-dimensional dataset.