用多领域经验贝叶斯提升因果表示学习的估计精度。
Multi-Domain Empirical Bayes for Linearly-Mixed Causal Representations
- 基于因果结构的分数匹配，利用跨域不变性优化表示学习
- 在已知图结构和干预目标时，比现有方法更准确地估计因果变量
- 适合关注因果建模与跨域泛化的研究人员
因果表示学习（CRL）旨在从高维观测中学习低维因果潜在变量。尽管可识别性已被广泛研究，但估计问题仍缺乏探索。本文探讨使用经验贝叶斯（EB）估计因果表示。特别地，考虑来自多个领域数据的学习问题，其中领域间差异由共享因果模型中的干预所驱动。多领域CRL自然形成一个联合推断问题，正契合经验贝叶斯的设计目标。我们提出一种基于EB的f-建模算法，通过利用域内与域间不变结构来提升学习到的因果变量质量。具体而言，假设线性测量模型及来自共享无环结构因果模型的干预先验。当图结构和干预目标已知时，我们设计了一种基于因果结构化分数匹配的EM型算法。此外，讨论了在现有CRL方法框架下的EB g-建模。在合成数据上的实验表明，该方法在因果表示估计上优于其他方法。
原文摘要 · Abstract (English)
Causal representation learning (CRL) aims to learn low-dimensional causal latent variables from high-dimensional observations. While identifiability has been extensively studied for CRL, estimation has been less explored. In this paper, we explore the use of empirical Bayes (EB) to estimate causal representations. In particular, we consider the problem of learning from data from multiple domains, where differences between domains are modeled by interventions in a shared underlying causal model. Multi-domain CRL naturally poses a simultaneous inference problem that EB is designed to tackle. Here, we propose an EB $f$-modeling algorithm that improves the quality of learned causal variables by exploiting invariant structure within and across domains. Specifically, we consider a linear measurement model and interventional priors arising from a shared acyclic SCM. When the graph and intervention targets are known, we develop an EM-style algorithm based on causally structured score matching. We further discuss EB $g$-modeling in the context of existing CRL approaches. In experiments on synthetic data, our proposed method achieves more accurate estimation than other methods for CRL.
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