Large Linear Multi-output Gaussian Process Learning

Abstract

Gaussian process (GP) models, which put a distribution over arbitrary functions in a continuous domain, can be generalized to the multi-output case; a common way of doing this is to use a linear model of coregionalization. Such models can learn correlations across the multiple outputs, which can then be exploited to share knowledge across the multiple outputs. For instance, temperature data from disparate regions over time can contribute to a predictive weather model that is more accurate than the same model applied to a single region. While model learning can be performed efficiently for single-output GPs, the multi-output case still requires approximations for large numbers of observations across all outputs. In this work, we propose a new method, Large Linear GP (LLGP), which estimates covariance hyperparameters for multi-dimensional outputs and one-dimensional inputs. Our approach learns GP kernel hyperparameters at an asymptotically faster rate than the current state of the art. When applied to real time series data, we find this theoretical improvement is realized with LLGP being generally an order of magnitude faster while improving or maintaining predictive accuracy. Finally, we discuss extensions of our approach to multidimensional inputs.