Iterative Sketching for Secure Coded Regression

TL;DR

This paper introduces a novel iterative sketching method for secure distributed linear regression that combines randomized basis rotation and subsampling to enhance security, reduce computation, and improve efficiency in asynchronous systems.

Contribution

It presents a new approach that integrates randomized basis rotation with subsampling to secure and accelerate distributed linear regression, ensuring straggler resiliency.

Findings

Achieves secure data encoding through basis rotation.

Reduces problem dimension via subsampling.

Provides an iterative stochastic framework for efficient regression.

Abstract

Linear regression is a fundamental and primitive problem in supervised machine learning, with applications ranging from epidemiology to finance. In this work, we propose methods for speeding up distributed linear regression. We do so by leveraging randomized techniques, while also ensuring security and straggler resiliency in asynchronous distributed computing systems. Specifically, we randomly rotate the basis of the system of equations and then subsample blocks, to simultaneously secure the information and reduce the dimension of the regression problem. In our setup, the basis rotation corresponds to an encoded encryption in an approximate gradient coding scheme, and the subsampling corresponds to the responses of the non-straggling servers in the centralized coded computing framework. This results in a distributive iterative stochastic approach for matrix compression and steepest descent.