Interventional Causal Representation Learning
Interventional Causal Representation Learning
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DOI：
10.48550/arxiv.2209.11924
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发表时间：
2022-09
期刊：
影响因子：
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通讯作者：
Kartik Ahuja;Yixin Wang;Divyat Mahajan;Y. Bengio
中科院分区：
文献类型：
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作者：
Kartik Ahuja;Yixin Wang;Divyat Mahajan;Y. Bengio
因果表征学习旨在从低层次的感觉数据中提取高层次的潜在因素。大多数现有方法依赖于观测数据和结构假设（如条件独立性）来识别潜在因素。然而，介入性数据在各种应用中普遍存在。干预性数据能促进因果表征学习吗？本文对这一问题进行了探讨。关键的观察结果是，干预数据通常带有潜在因素支持的几何特征（即每个潜在因素可能采取的值）。例如，当潜在因素之间存在因果联系时，干预可以打破被干预潜在因素与其祖先之间的依赖关系。利用这一事实，我们证明了从完美的$do$干预中获得的数据，可以识别出潜在的因果因素，直至排列和缩放。此外，我们可以实现块仿射识别，即如果我们能够从不完善的干预中获得数据，则估计的潜在因素仅与其他几个潜在因素纠缠。这些结果突出了介入数据在因果表征学习中的独特力量；它们可以对潜在因素进行可证明的识别，而无需对其分布或依赖结构进行任何假设。
Causal representation learning seeks to extract high-level latent factors from low-level sensory data. Most existing methods rely on observational data and structural assumptions (e.g., conditional independence) to identify the latent factors. However, interventional data is prevalent across applications. Can interventional data facilitate causal representation learning? We explore this question in this paper. The key observation is that interventional data often carries geometric signatures of the latent factors' support (i.e. what values each latent can possibly take). For example, when the latent factors are causally connected, interventions can break the dependency between the intervened latents' support and their ancestors'. Leveraging this fact, we prove that the latent causal factors can be identified up to permutation and scaling given data from perfect $do$ interventions. Moreover, we can achieve block affine identification, namely the estimated latent factors are only entangled with a few other latents if we have access to data from imperfect interventions. These results highlight the unique power of interventional data in causal representation learning; they can enable provable identification of latent factors without any assumptions about their distributions or dependency structure.