Indiscriminate Disruption of Conditional Inference on Multivariate Gaussians

TL;DR

This paper investigates how an adversary can disrupt conditional inference in multivariate Gaussian models, revealing vulnerabilities and attack strategies across various real-world applications.

Contribution

It introduces a novel framework for adversarial attacks on Gaussian inference, analyzing white- and grey-box scenarios with structural solution insights.

Findings

Attacks can significantly impair inference accuracy.

White-box and grey-box attack behaviors differ under uncertainty.

The methods are applicable to diverse real-world problems.

Abstract

The multivariate Gaussian distribution underpins myriad operations-research, decision-analytic, and machine-learning models (e.g., Bayesian optimization, Gaussian influence diagrams, and variational autoencoders). However, despite recent advances in adversarial machine learning (AML), inference for Gaussian models in the presence of an adversary is notably understudied. Therefore, we consider a self-interested attacker who wishes to disrupt a decisionmaker's conditional inference and subsequent actions by corrupting a set of evidentiary variables. To avoid detection, the attacker also desires the attack to appear plausible wherein plausibility is determined by the density of the corrupted evidence. We consider white- and grey-box settings such that the attacker has complete and incomplete knowledge about the decisionmaker's underlying multivariate Gaussian distribution, respectively. Select instances are shown to reduce to quadratic and stochastic quadratic programs, and structural properties are derived to inform solution methods. We assess the impact and efficacy of these attacks in three examples, including, real estate evaluation, interest rate estimation and signals processing. Each example leverages an alternative underlying model, thereby highlighting the attacks' broad applicability. Through these applications, we also juxtapose the behavior of the white- and grey-box attacks to understand how uncertainty and structure affect attacker behavior.