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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.