Graduate School and Research Center in Digital Sciences

Entropic trace estimates for log determinants

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

ECML/PKDD 2017, European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, September 18-22, 2017, Skopje, Macedonia

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 elds, 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 signi cant 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 eld, we also demonstrate how this approach can signi cantly accelerate inference in large-scale learning methods involving the log determinant.

Document Arxiv Bibtex

Title:Entropic trace estimates for log determinants
Department:Data Science
Eurecom ref:5265
Bibtex: @inproceedings{EURECOM+5265, year = {2017}, title = {{E}ntropic trace estimates for log determinants}, author = {{F}itzsimons, {J}ack and {G}ranziol, {D}iego and {C}utajar, {K}urt and {O}sborne, {M}ichael and {F}ilippone, {M}aurizio and {R}oberts, {S}tephen}, booktitle = {{ECML}/{PKDD} 2017, {E}uropean {C}onference on {M}achine {L}earning and {P}rinciples and {P}ractice of {K}nowledge {D}iscovery in {D}atabases, {S}eptember 18-22, 2017, {S}kopje, {M}acedonia }, address = {{S}kopje, {MACEDONIA}, {THE} {FORMER} {YUGOSLAV} {REPUBLIC} {OF}}, month = {09}, url = {} }
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