An Efficient Reversible Algorithm for Linear Regression

TL;DR

This paper introduces a reversible algorithm for linear regression that matches the efficiency of traditional methods, expanding reversible matrix operations to rectangular matrices and inversion.

Contribution

The paper develops a reversible algorithm for linear regression, including ridge regression, with optimal asymptotic complexity, extending reversible matrix multiplication and inversion techniques.

Findings

Reversible algorithm matches standard algorithms in time and space complexity.

Extended reversible matrix multiplication to rectangular matrices.

Achieved reversible matrix inversion with comparable efficiency.

Abstract

This paper presents an efficient reversible algorithm for linear regression, both with and without ridge regression. Our reversible algorithm matches the asymptotic time and space complexity of standard irreversible algorithms for this problem. Needed for this result is the expansion of the analysis of efficient reversible matrix multiplication to rectangular matrices and matrix inversion.