Lambert matrix factorization

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Abstract

Many data generating processes result in skewed data, which should be modeled by distributions that can capture the skewness. In this work we adopt the flexible family of Lambert W distributions that combine arbitrary standard distribution with specific nonlinear transformation to incorporate skewness. We describe how Lambert W distributions can be used in probabilistic programs by providing stable gradient-based inference, and demonstrate their use in matrix factorization. In particular, we focus in modeling logarithmically transformed count data. We analyze the weighted squared loss used by state-of-the-art word embedding models to learn interpretable representations from word co-occurrences and show that a generative model capturing the essential properties of those models can be built using Lambert W distributions.
Original languageEnglish
Title of host publicationMachine Learning and Knowledge Discovery in Databases : European Conference, ECML PKDD 2018, Dublin, Ireland, September 10–14, 2018, Proceedings, Part II
EditorsMichele Berlingerio, Francesco Bonchi, Thomas Gärtner, Neil Hurley, Georgiana Ifrim
Number of pages17
Place of PublicationCham
PublisherSpringer Nature Switzerland
Publication date2019
Pages311-326
ISBN (Print)978-3-030-10927-1
ISBN (Electronic)978-3-030-10928-8
Publication statusPublished - 2019
MoE publication typeA4 Article in conference proceedings
EventECML PKDD: Joint European Conference on Machine Learning and Knowledge Discovery in Databases - Dublin, Ireland
Duration: 10 Sep 201814 Sep 2018
http://www.ecmlpkdd2018.org/

Publication series

NameLecture Notes in Artificial Intelligence
Volume11052
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Fields of Science

  • 113 Computer and information sciences

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