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Gauss quadrature for matrix inverse forms with applications

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dc.contributor.author Li, Chengtao
dc.contributor.author Sra, Suvrit
dc.contributor.author Jegelka, Stefanie Sabrina
dc.date.accessioned 2017-12-29T21:19:17Z
dc.date.available 2017-12-29T21:19:17Z
dc.date.issued 2016-06
dc.identifier.uri http://hdl.handle.net/1721.1/113000
dc.description.abstract We present a framework for accelerating a spectrum of machine learning algorithms that require computation of bilinear inverse forms u[superscript T] A[superscript −1]u, where A is a positive definite matrix and u a given vector. Our framework is built on Gauss-type quadrature and easily scales to large, sparse matrices. Further, it allows retrospective computation of lower and upper bounds on u[superscript T] > A[superscript −1]u, which in turn accelerates several algorithms. We prove that these bounds tighten iteratively and converge at a linear (geometric) rate. To our knowledge, ours is the first work to demonstrate these key properties of Gauss-type quadrature, which is a classical and deeply studied topic. We illustrate empirical consequences of our results by using quadrature to accelerate machine learning tasks involving determinantal point processes and submodular optimization, and observe tremendous speedups in several instances. en_US
dc.description.sponsorship Google (Research Award) en_US
dc.description.sponsorship National Science Foundation (U.S.) (CAREER Award 1553284) en_US
dc.language.iso en_US
dc.publisher Proceedings of Machine Learning Research en_US
dc.relation.isversionof http://proceedings.mlr.press/v48 en_US
dc.rights Creative Commons Attribution-Noncommercial-Share Alike en_US
dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/4.0/ en_US
dc.source arXiv en_US
dc.title Gauss quadrature for matrix inverse forms with applications en_US
dc.type Article en_US
dc.identifier.citation Li, Chengtao, Suvrit Sra, and Stefanie Jegelka. "Gauss quadrature for matrix inverse forms with applications." International Conference on Machine Learning, 20-22 June 2016, New York, New York, PMLR, 2016. en_US
dc.contributor.department Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science en_US
dc.contributor.department Massachusetts Institute of Technology. Laboratory for Information and Decision Systems en_US
dc.contributor.mitauthor Li, Chengtao
dc.contributor.mitauthor Sra, Suvrit
dc.contributor.mitauthor Jegelka, Stefanie Sabrina
dc.relation.journal International Conference on Machine Learning en_US
dc.identifier.mitlicense OPEN_ACCESS_POLICY en_US
dc.eprint.version Original manuscript en_US
dc.type.uri http://purl.org/eprint/type/ConferencePaper en_US
eprint.status http://purl.org/eprint/status/NonPeerReviewed en_US
dspace.orderedauthors Li, Chengtao; Sra, Suvrit; Jegelka, Stefanie en_US
dspace.embargo.terms N en_US
dc.identifier.orcid https://orcid.org/0000-0003-1532-3083
dc.identifier.orcid https://orcid.org/0000-0001-8516-4925
dc.identifier.orcid https://orcid.org/0000-0002-6121-9474


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