Entropic Trace Estimates for Log Determinants

Jack Fitzsimons*, Diego Granziol, Kurt Cutajar, Michael Osborne, Maurizio Filippone, Stephen Roberts

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

11 Scopus citations

Abstract

The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models and many others. In this work, we estimate log determinants under the framework of maximum entropy, given information in the form of moment constraints from stochastic trace estimation. The estimates demonstrate a significant improvement on state-of-the-art alternative methods, as shown on a wide variety of matrices from the SparseSuite Matrix Collection. By taking the example of a general Markov random field, we also demonstrate how this approach can significantly accelerate inference in large-scale learning methods involving the log determinant.

Original languageEnglish (US)
Title of host publicationMachine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2017, Proceedings
EditorsMichelangelo Ceci, Saso Dzeroski, Celine Vens, Ljupco Todorovski, Jaakko Hollmen
PublisherSpringer Verlag
Pages323-338
Number of pages16
ISBN (Print)9783319712482
DOIs
StatePublished - 2017
EventEuropean Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2017 - Skopje, Macedonia, The Former Yugoslav Republic of
Duration: Sep 18 2017Sep 22 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10534 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceEuropean Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2017
Country/TerritoryMacedonia, The Former Yugoslav Republic of
CitySkopje
Period09/18/1709/22/17

Bibliographical note

Publisher Copyright:
© 2017, Springer International Publishing AG.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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