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Scalable Log Determinants for Gaussian Process Kernel Learning
Kun Dong · David Eriksson · Hannes Nickisch · David Bindel · Andrew Wilson

Tue Dec 05 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #196 #None

For applications as varied as Bayesian neural networks, determinantal point processes, elliptical graphical models, and kernel learning for Gaussian processes (GPs), one must compute a log determinant of an n by n positive definite matrix, and its derivatives---leading to prohibitive O(n^3) computations. We propose novel O(n) approaches to estimating these quantities from only fast matrix vector multiplications (MVMs). These stochastic approximations are based on Chebyshev, Lanczos, and surrogate models, and converge quickly even for kernel matrices that have challenging spectra. We leverage these approximations to develop a scalable Gaussian process approach to kernel learning. We find that Lanczos is generally superior to Chebyshev for kernel learning, and that a surrogate approach can be highly efficient and accurate with popular kernels.

Author Information

Kun Dong (Cornell University)
David Eriksson (Cornell University)
Hannes Nickisch (Philips Research)
David Bindel (Cornell University)
Andrew Wilson (Cornell University)

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