TY - GEN

T1 - Polynomial tensor sketch for element-wise function of low-rank matrix

AU - Han, Insu

AU - Avron, Haim

AU - Shin, Jinwoo

N1 - Publisher Copyright:
© International Conference on Machine Learning, ICML 2020. All rights reserved.

PY - 2020

Y1 - 2020

N2 - This 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 highrank) 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.

AB - This 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 highrank) 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.

UR - http://www.scopus.com/inward/record.url?scp=85105257607&partnerID=8YFLogxK

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AN - SCOPUS:85105257607

T3 - 37th International Conference on Machine Learning, ICML 2020

SP - 3942

EP - 3951

BT - 37th International Conference on Machine Learning, ICML 2020

A2 - Daume, Hal

A2 - Singh, Aarti

PB - International Machine Learning Society (IMLS)

T2 - 37th International Conference on Machine Learning, ICML 2020

Y2 - 13 July 2020 through 18 July 2020

ER -