Testing sparsity over known and unknown bases

Barman, S and Bhattacharyya, A and Ghoshal, S (2018) Testing sparsity over known and unknown bases. In: 35th International Conference on Machine Learning, ICML 2018, 10 - 15 July 2018, Stockholm, pp. 819-843.

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Abstract

Sparsity is a basic property of real vectors that is exploited in a wide variety of machine learning applications. In this work, we describe property testing algorithms for sparsity that observe a lowdimensional projection of the input. We consider two settings. In the first setting, we test sparsity with respect to an unknown basis: given input vectors y1, . . . , yp ∈ R d whose concatenation as columns forms Y ∈ R d×p , does Y = AX for matrices A ∈ R d×m and X ∈ R m×p such that each column of X is k-sparse, or is Y far from having such a decomposition? In the second setting, we test sparsity with respect to a known basis: for a fixed design matrix A ∈ R d×m, given input vector y ∈ R d , is y = Ax for some ksparse vector x or is y far from having such a decomposition? We analyze our algorithms using tools from high-dimensional geometry and probability.

Item Type:	Conference Paper
Publication:	35th International Conference on Machine Learning, ICML 2018
Publisher:	International Machine Learning Society (IMLS)
Additional Information:	The copyright for this article belongs to the International Machine Learning Society (IMLS).
Keywords:	Artificial intelligence; Vectors, Design matrix; High-dimensional; Input vector; Machine learning applications; Property-testing; Real vector, Learning systems
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	19 Aug 2022 05:22
Last Modified:	19 Aug 2022 05:22
URI:	https://eprints.iisc.ac.in/id/eprint/75984

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