Polynomial Tensor Sketch for Element-wise Function of Low-Rank Matrix

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dc.contributor.authorHan, Insuko
dc.contributor.authorAvron, Haimko
dc.contributor.authorShin, Jinwooko
dc.date.accessioned2020-12-15T06:30:30Z-
dc.date.available2020-12-15T06:30:30Z-
dc.date.created2020-12-02-
dc.date.created2020-12-02-
dc.date.issued2020-07-15-
dc.identifier.citationThirty-seventh International Conference on Machine Learning, ICML 2020, pp.3942 - 3951-
dc.identifier.issn2640-3498-
dc.identifier.urihttp://hdl.handle.net/10203/278494-
dc.description.abstractThis paper studies how to sketch element-wise functions of low-rank matrices. Formally, given low-rank matrix A = [Aij] and scalar non-linear function f, we aim for finding an approximated low-rank representation of the (possibly high-rank) matrix [f(Aij)]. To this end, we propose an efficient sketching-based algorithm whose complexity is significantly lower than the number of entries of A, i.e., it runs without accessing all entries of [f(Aij)] explicitly. The main idea underlying our method is to combine a polynomial approximation of f with the existing tensor sketch scheme for approximating monomials of entries of A. To balance the errors of the two approximation components in an optimal manner, we propose a novel regression formula to find polynomial coefficients given A and f. In particular, we utilize a coreset-based regression with a rigorous approximation guarantee. Finally, we demonstrate the applicability and superiority of the proposed scheme under various machine learning tasks.-
dc.languageEnglish-
dc.publisherInternational Conference on Machine Learning-
dc.titlePolynomial Tensor Sketch for Element-wise Function of Low-Rank Matrix-
dc.typeConference-
dc.identifier.wosid000683178504010-
dc.identifier.scopusid2-s2.0-85105257607-
dc.type.rimsCONF-
dc.citation.beginningpage3942-
dc.citation.endingpage3951-
dc.citation.publicationnameThirty-seventh International Conference on Machine Learning, ICML 2020-
dc.identifier.conferencecountryAU-
dc.identifier.conferencelocationVirtual-
dc.contributor.localauthorShin, Jinwoo-
dc.contributor.nonIdAuthorAvron, Haim-
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