对抗性因果干预证伪

中文摘要 AI 辅助

生成模型可重现观测分布，却编码了错误的因果结构。本文研究一个序贯博弈：结构因果生成器提出观测分布与干预分布，对抗性实验者选择干预措施以最大化证伪生成器。该判别器并非简单的真实与合成分类器，而是以干预为索引，测试生成器是否重现对应干预后规律。本文引入对抗性因果干预证伪（ACIF），构建该博弈的神谕版本与可实现版本，并区分常被混淆的三类对象：观测拟合、可容许查询类上的干预等价性，以及结构因果模型的点识别。针对有限模型类与干预类，本文证明：（i）对抗目标可精确归约为最坏干预积分概率度量；（ii）在干预等价意义下可实现识别，若存在可分干预族则可实现点识别；（iii）存在混合策略均衡；（iv）有限样本一致收敛性与基于间隔的模型选择保证；（v）在平衡可分条件下，基于分歧驱动的序贯设计可实现对数级消除保证。本文还给出一个完整的线性高斯示例：两个观测上不可区分的因果方向，可通过单个精心选择的干预实现区分。该框架阐明了对抗性因果判别器可认证与不可认证的内容，为因果生成建模、主动因果发现与实验设计提供了原则性桥梁。

英文摘要

Generative models can reproduce an observational distribution while encoding an incorrect causal structure. We study a sequential game in which a structural causal generator proposes observational and interventional distributions, while an adversarial experimentalist selects interventions intended to maximally falsify the generator. The discriminator is therefore not merely a real-versus-synthetic classifier: it is indexed by an intervention and tests whether the generator reproduces the corresponding post-intervention law. We introduce Adversarial Causal Intervention Falsification (ACIF), formulate oracle and implementable versions of the game, and distinguish three objects that are often conflated: observational fit, interventional equivalence over an admissible query class, and point identification of a structural causal model. For finite model and intervention classes, we prove: (i) an exact reduction of the adversarial objective to a worst-intervention integral probability metric; (ii) identification up to interventional equivalence, with point identification under a separating intervention family; (iii) existence of mixed-strategy equilibria; (iv) finite-sample uniform convergence and margin-based model-selection guarantees; and (v) a logarithmic elimination guarantee for a disagreement-driven sequential design under a balanced-separation condition. We also give a complete linear-Gaussian example in which two observationally indistinguishable causal directions are separated by a single well-chosen intervention. The framework clarifies what an adversarial causal discriminator can and cannot certify, and provides a principled bridge between causal generative modeling, active causal discovery, and experimental design.

发表机构

• University of Calgary（卡尔加里大学）

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