Ecole d'ingénieur et centre de recherche en Sciences du numérique

Bayesian inference of log determinants

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

UAI 2017, Conference on Uncertainty in Artificial Intelligence, August 11-15, 2017, Sydney, Australia

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.

Document Arxiv Bibtex

Titre:Bayesian inference of log determinants
Type:Conférence
Langue:English
Ville:Sydney
Pays:AUSTRALIE
Date:
Département:Data Science
Eurecom ref:5186
Copyright: © EURECOM. Personal use of this material is permitted. The definitive version of this paper was published in UAI 2017, Conference on Uncertainty in Artificial Intelligence, August 11-15, 2017, Sydney, Australia and is available at :
Bibtex: @inproceedings{EURECOM+5186, year = {2017}, title = {{B}ayesian inference of log determinants}, author = {{F}itzsimons, {J}ack and {C}utajar, {K}urt and {O}sborne, {M}ichael and {R}oberts, {S}tephen and {F}ilippone, {M}aurizio}, booktitle = {{UAI} 2017, {C}onference on {U}ncertainty in {A}rtificial {I}ntelligence, {A}ugust 11-15, 2017, {S}ydney, {A}ustralia}, address = {{S}ydney, {AUSTRALIE}}, month = {08}, url = {http://www.eurecom.fr/publication/5186} }
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