Recent progress in Neural Causal Models (NCMs) showcased how identification
and partial identification of causal effects can be automatically carried out
via training of neural generative models that respect the constraints encoded
in a given causal graph [Xia et al. 2022, Balazadeh et al. 2022]. However,
formal consistency of these methods has only been proven for the case of
discrete variables or only for linear causal models. In this work, we prove
consistency of partial identification via NCMs in a general setting with both
continuous and categorical variables. Further, our results highlight the impact
of the design of the underlying neural network architecture in terms of depth
and connectivity as well as the importance of applying Lipschitz regularization
in the training phase. In particular, we provide a counterexample showing that
without Lipschitz regularization the NCM may not be asymptotically consistent.
Our results are enabled by new results on the approximability of structural
causal models via neural generative models, together with an analysis of the
sample complexity of the resulting architectures and how that translates into
an error in the constrained optimization problem that defines the partial
identification bounds.

Neural Causal Models (NCMs) 是用于自动识别和部分识别因果效应的神经生成模型的研究。本研究证明了在具有连续和分类变量的一般情况下，通过 NCMs 进行部分识别的一致性，并强调了神经网络架构的设计、深度和连接性以及训练阶段应用 Lipschitz 正则化的重要性。

神经因果部分识别的一致性

Consistency of Neural Causal Partial Identification

The abilities of humans to understand the world in terms of cause and effect
relationships, as well as to compress information into abstract concepts, are
two hallmark features of human intelligence. These two topics have been studied
in tandem in the literature under the rubric of causal abstractions theory. In
practice, it remains an open problem how to best leverage abstraction theory in
real-world causal inference tasks, where the true mechanisms are unknown and
only limited data is available. In this paper, we develop a new family of
causal abstractions by clustering variables and their domains. This approach
refines and generalizes previous notions of abstractions to better accommodate
individual causal distributions that are spawned by Pearl's causal hierarchy.
We show that such abstractions are learnable in practical settings through
Neural Causal Models (Xia et al., 2021), enabling the use of the deep learning
toolkit to solve various challenging causal inference tasks -- identification,
estimation, sampling -- at different levels of granularity. Finally, we
integrate these results with representation learning to create more flexible
abstractions, moving these results closer to practical applications. Our
experiments support the theory and illustrate how to scale causal inferences to
high-dimensional settings involving image data.

通过聚类变量及其域的方法，发展了一种新的因果抽象方法，以更好地适应由 Pearl 的因果层次结构引发的个体因果分布，并进一步将这些结果与表示学习相结合，将这些结果更接近实际应用。

神经因果抽象

Neural Causal Abstractions

Learning models that offer robust out-of-distribution generalization and fast
adaptation is a key challenge in modern machine learning. Modelling causal
structure into neural networks holds the promise to accomplish robust zero and
few-shot adaptation. Recent advances in differentiable causal discovery have
proposed to factorize the data generating process into a set of modules, i.e.
one module for the conditional distribution of every variable where only causal
parents are used as predictors. Such a modular decomposition of knowledge
enables adaptation to distributions shifts by only updating a subset of
parameters. In this work, we systematically study the generalization and
adaption performance of such modular neural causal models by comparing it to
monolithic models and structured models where the set of predictors is not
constrained to causal parents. Our analysis shows that the modular neural
causal models outperform other models on both zero and few-shot adaptation in
low data regimes and offer robust generalization. We also found that the
effects are more significant for sparser graphs as compared to denser graphs.

本文研究了神经因果模型在零样本和小样本情况下的性能，并将其与单体模型和结构模型进行比较，其中预测变量的集合没有被限制为因果父节点。研究发现，相对于其他模型，因果神经模型在低数据量情况下具有更好的零样本和小样本适应性，并提供了稳健的泛化能力。此外，研究发现，比起更密集的图，对于更稀疏的图，这种效果更为显著。