Large Linear Multi-output Gaussian Process Learning

Vladimir Feinberg; Li-Fang Cheng; Kai Li; Barbara E Engelhardt

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arXiv · 1705.10813

Large Linear Multi-output Gaussian Process Learning

Vladimir Feinberg·Li-Fang Cheng·Kai Li·Barbara E Engelhardt

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Abstract

Gaussian processes (GPs), or distributions over arbitrary functions in a continuous domain, can be generalized to the multi-output case: a linear model of coregionalization (LMC) is one approach. LMCs estimate and exploit correlations across the multiple outputs. While model estimation can be performed efficiently for single-output GPs, these assume stationarity, but in the multi-output case the cross-covariance interaction is not stationary. We propose Large Linear GP (LLGP), which circumvents the need for stationarity by inducing structure in the LMC kernel through a common grid of inputs shared between outputs, enabling optimization of GP hyperparameters for multi-dimensional outputs and low-dimensional inputs. When applied to synthetic two-dimensional and real time series data, we find our theoretical improvement relative to the current solutions for multi-output GPs is realized with LLGP reducing training time while improving or maintaining predictive mean accuracy. Moreover, by using a direct likelihood approximation rather than a variational one, model confidence estimates are significantly improved.

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BibTeX RIS

Vladimir Feinberg, Li-Fang Cheng, Kai Li, Barbara E Engelhardt. 2017-05-30. Large Linear Multi-output Gaussian Process Learning. https://arxiv.org/abs/1705.10813

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