One of the most compelling features of Gaussian process (GP) regression is its ability to provide well-calibrated posterior distributions. Recent advances in inducing point methods have sped up GP marginal likelihood and posterior mean computations, leaving posterior covariance estimation and sampling as the remaining computational bottlenecks. In this paper we address these shortcomings by using the Lanczos algorithm to rapidly approximate the predictive covariance matrix. Our approach, which we refer to as LOVE (LanczOs Variance Estimates), substantially improves time and space complexity. In our experiments, LOVE computes covariances up to 2,000 times faster and draws samples 18,000 times faster than existing methods, all without sacrificing accuracy.
Author Information
Geoff Pleiss (Cornell University)
Jacob Gardner (Uber AI Labs)
Kilian Weinberger (Cornell University)
Kilian Weinberger is an Associate Professor in the Department of Computer Science at Cornell University. He received his Ph.D. from the University of Pennsylvania in Machine Learning under the supervision of Lawrence Saul and his undergraduate degree in Mathematics and Computer Science from the University of Oxford. During his career he has won several best paper awards at ICML, CVPR, AISTATS and KDD (runner-up award). In 2011 he was awarded the Outstanding AAAI Senior Program Chair Award and in 2012 he received an NSF CAREER award. He was elected co-Program Chair for ICML 2016 and for AAAI 2018. Kilian Weinberger's research focuses on Machine Learning and its applications. In particular, he focuses on learning under resource constraints, metric learning, machine learned web-search ranking, computer vision and deep learning. Before joining Cornell University, he was an Associate Professor at Washington University in St. Louis and before that he worked as a research scientist at Yahoo! Research in Santa Clara.
Andrew Wilson (Cornell University)
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