Modeling true world data-generating processes lies at the heart of empirical science. Structural Causal Models (SCMs) and their associated Directed Acyclic Graphs (DAGs) provide an increasingly popular answer to such problems by defining the causal generative process that transforms random noise into observations. However, learning them from observational data poses an ill-posed and NP-hard inverse problem in general. In this work, we propose a new and equivalent formalism that do not require DAGs to describe them, viewed as fixed-point problems on the causally ordered variables, and show three important cases where they can be uniquely recovered given the topological ordering (TO). To the best of our knowledge, we obtain the most general recovery results when the TO is known. Based on our theoretical findings, we design a two-stage causal generative model that first infers the causal order from observations in a zero-shot manner, thus by-passing the search, and then learns the generative fixed-point SCM on the ordered variables. To infer TOs from observations, we propose to amortize the learning of TOs on generated datasets by sequentially predicting the leaves of graphs seen during training. To learn fixed-point SCMs, we design a transformer-based architecture that exploits a new attention mechanism enabling the modeling of causal structures, and show that this parameterization is consistent with our formalism. Finally, we conduct an extensive evaluation of each method individually, and show that when combined, our model outperforms various baselines on generated out-of-distribution problems.

基于新的等效形式主义，提出了一种新的因果生成模型，利用拓扑排序从观测值中推断顺序，设计了基于Transformer的架构来学习固定点结构因果模型，并通过广泛的评估表明该模型在生成的超出分布问题中胜过多个基准模型。

FiP: 因果生成建模的固定点方法