Empirical Perturbation Analysis of Linear System Solvers from a Data Poisoning Perspective

TL;DR

This paper investigates how linear system solvers respond to data poisoning attacks, analyzing the impact of adversarial perturbations on solution accuracy and proposing methods to improve robustness.

Contribution

It introduces a data poisoning perspective to perturbation analysis of linear solvers, proposing new perturbation methods and analyzing solver robustness under adversarial attacks.

Findings

Different solvers exhibit varying sensitivity to data poisoning.

Proposed perturbation methods reveal vulnerabilities in common linear solvers.

Insights guide development of more robust linear system algorithms.

Abstract

The perturbation analysis of linear solvers applied to systems arising broadly in machine learning settings -- for instance, when using linear regression models -- establishes an important perspective when reframing these analyses through the lens of a data poisoning attack. By analyzing solvers' responses to such attacks, this work aims to contribute to the development of more robust linear solvers and provide insights into poisoning attacks on linear solvers. In particular, we investigate how the errors in the input data will affect the fitting error and accuracy of the solution from a linear system-solving algorithm under perturbations common in adversarial attacks. We propose data perturbation through two distinct knowledge levels, developing a poisoning optimization and studying two methods of perturbation: Label-guided Perturbation (LP) and Unconditioning Perturbation (UP). Existing works mainly focus on deriving the worst-case perturbation bound from a theoretical perspective, and the analysis is often limited to specific kinds of linear system solvers. Under the circumstance that the data is intentionally perturbed -- as is the case with data poisoning -- we seek to understand how different kinds of solvers react to these perturbations, identifying those algorithms most impacted by different types of adversarial attacks.