arXiv:2411.14351stat.MLcs.CR2024-11

攻击者通过伪造证据干扰高斯模型推理,让决策失效且不被察觉。

Indiscriminate Disruption of Conditional Inference on Multivariate Gaussians

  • 设计白盒与灰盒攻击,用密度控制伪造证据的合理性。
  • 攻击可转化为二次规划问题,在真实场景中显著误导决策结果。
  • 适用于房地产评估等多领域,揭示不确定性对攻击策略的影响。

多元高斯分布广泛应用于运筹、决策分析和机器学习模型(如贝叶斯优化、高斯影响图、变分自编码器)。然而,尽管对抗机器学习已有进展,针对高斯模型在对抗环境下的推理研究仍不足。本文研究自利攻击者通过污染证据变量,干扰决策者的条件推断及后续行为,同时避免被发现——即攻击需符合证据的密度分布。考虑白盒(完全已知)与灰盒(部分已知)情形,攻击可归约为二次规划与随机二次规划问题,导出结构性质以指导求解。在房地产估值、利率估算和信号处理三个实例中验证攻击效果,涵盖不同底层模型,体现其广泛应用性。对比白盒与灰盒攻击行为,揭示不确定性和结构如何影响攻击策略。

原文摘要 · Abstract (English)

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.

对抗攻击高斯模型决策干扰可解释性

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