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

FiP: a Fixed-Point Approach for Causal Generative Modeling

We consider the problem of inference in a causal generative model where the
set of available observations differs between data instances. We show how
combining samples drawn from the graphical model with an appropriate masking
function makes it possible to train a single neural network to approximate all
the corresponding conditional marginal distributions and thus amortize the cost
of inference. We further demonstrate that the efficiency of importance sampling
may be improved by basing proposals on the output of the neural network. We
also outline how the same network can be used to generate samples from an
approximate joint posterior via a chain decomposition of the graph.

本文研究了在因果生成模型中进行推断的问题，通过从图形模型中提取样本，结合适当的屏蔽函数，可以训练单个神经网络来近似所有相应的条件边缘分布，从而摊销推断成本，并通过图的链式分解来从近似联合后验中生成样本。