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

Fuente: arXiv
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Main Authors: Liu, Yixin, Carr, Arielle, Sun, Lichao
Format: Preprint
Published: 2024
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author Liu, Yixin
Carr, Arielle
Sun, Lichao
author_facet Liu, Yixin
Carr, Arielle
Sun, Lichao
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_00878
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Empirical Perturbation Analysis of Linear System Solvers from a Data Poisoning Perspective
Liu, Yixin
Carr, Arielle
Sun, Lichao
Machine Learning
Cryptography and Security
Numerical Analysis
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.
title Empirical Perturbation Analysis of Linear System Solvers from a Data Poisoning Perspective
topic Machine Learning
Cryptography and Security
Numerical Analysis
url https://arxiv.org/abs/2410.00878