Secure Linear MDS Coded Matrix Inversion

Neophytos Charalambides; Mert Pilanci; Alfred Hero

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arXiv · 2207.06271

Secure Linear MDS Coded Matrix Inversion

Neophytos Charalambides·Mert Pilanci·Alfred Hero

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Abstract

A cumbersome operation in many scientific fields, is inverting large full-rank matrices. In this paper, we propose a coded computing approach for recovering matrix inverse approximations. We first present an approximate matrix inversion algorithm which does not require a matrix factorization, but uses a black-box least squares optimization solver as a subroutine, to give an estimate of the inverse of a real full-rank matrix. We then present a distributed framework for which our algorithm can be implemented, and show how we can leverage sparsest-balanced MDS generator matrices to devise matrix inversion coded computing schemes. We focus on balanced Reed-Solomon codes, which are optimal in terms of computational load; and communication from the workers to the master server. We also discuss how our algorithms can be used to compute the pseudoinverse of a full-rank matrix, and how the communication is secured from eavesdroppers.

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Neophytos Charalambides, Mert Pilanci, Alfred Hero. 2022-12-20. Secure Linear MDS Coded Matrix Inversion. https://arxiv.org/abs/2207.06271

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