Bayesian inference of log determinants

Jack Fitzsimons, Kurt Cutajar, Michael Osborne, Stephen Roberts, Maurizio Filippone

Research output: Contribution to conferencePaperpeer-review

8 Scopus citations


The log determinant of a kernel matrix appears in a variety of machine learning problems, ranging from determinantal point processes and generalized Markov random fields, through to the training of Gaussian processes. Exact calculation of this term is often intractable when the size of the kernel matrix exceeds a few thousands. In the spirit of probabilistic numerics, we reinterpret the problem of computing the log determinant as a Bayesian inference problem. In particular, we combine prior knowledge in the form of bounds from matrix theory and evidence derived from stochastic trace estimation to obtain probabilistic estimates for the log determinant and its associated uncertainty within a given computational budget. Beyond its novelty and theoretic appeal, the performance of our proposal is competitive with state-of-the-art approaches to approximating the log determinant, while also quantifying the uncertainty due to budgetconstrained evidence.

Original languageEnglish (US)
StatePublished - 2017
Event33rd Conference on Uncertainty in Artificial Intelligence, UAI 2017 - Sydney, Australia
Duration: Aug 11 2017Aug 15 2017


Conference33rd Conference on Uncertainty in Artificial Intelligence, UAI 2017

ASJC Scopus subject areas

  • Artificial Intelligence


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