Robust Certification for Laplace Learning on Geometric Graphs

TL;DR

This paper introduces the first adversarial robustness certification for Graph Laplacian-based semi-supervised learning classifiers, providing theoretical bounds and empirical validation to enhance security in graph-based ML tasks.

Contribution

It offers the first theoretical adversarial robustness certification for GL classifiers and demonstrates how existing defenses improve their robustness.

Findings

Theoretical bounds on classification accuracy difference post-attack.

Empirical validation confirms the certification's effectiveness.

Leveraging defenses from k-NN improves GL classifier robustness.

Abstract

Graph Laplacian (GL)-based semi-supervised learning is one of the most used approaches for classifying nodes in a graph. Understanding and certifying the adversarial robustness of machine learning (ML) algorithms has attracted large amounts of attention from different research communities due to its crucial importance in many security-critical applied domains. There is great interest in the theoretical certification of adversarial robustness for popular ML algorithms. In this paper, we provide the first adversarial robust certification for the GL classifier. More precisely we quantitatively bound the difference in the classification accuracy of the GL classifier before and after an adversarial attack. Numerically, we validate our theoretical certification results and show that leveraging existing adversarial defenses for the $k$-nearest neighbor classifier can remarkably improve the robustness of the GL classifier.