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DOI: 10.4230/LIPIcs.FSTTCS.2017.4
URN: urn:nbn:de:0030-drops-84193
URL: http://drops.dagstuhl.de/opus/volltexte/2018/8419/
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Shah, Devavrat

Matrix Estimation, Latent Variable Model and Collaborative Filtering

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LIPIcs-FSTTCS-2017-4.pdf (0.4 MB)


Abstract

Estimating a matrix based on partial, noisy observations is prevalent in variety of modern applications with recommendation system being a prototypical example. The non-parametric latent variable model provides canonical representation for such matrix data when the underlying distribution satisfies ``exchangeability'' with graphons and stochastic block model being recent examples of interest. Collaborative filtering has been a successfully utilized heuristic in practice since the dawn of e-commerce. In this extended abstract, we will argue that collaborative filtering (and its variants) solve matrix estimation for a generic latent variable model with near optimal sample complexity.

BibTeX - Entry

@InProceedings{shah:LIPIcs:2018:8419,
  author =	{Devavrat Shah},
  title =	{{Matrix Estimation, Latent Variable Model and Collaborative Filtering}},
  booktitle =	{37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)},
  pages =	{4:1--4:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-055-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{93},
  editor =	{Satya Lokam and R. Ramanujam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8419},
  URN =		{urn:nbn:de:0030-drops-84193},
  doi =		{10.4230/LIPIcs.FSTTCS.2017.4},
  annote =	{Keywords: Matrix Estimation, Graphon Estimation, Collaborative Filtering}
}

Keywords: Matrix Estimation, Graphon Estimation, Collaborative Filtering
Seminar: 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)
Issue Date: 2018
Date of publication: 26.01.2018


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