In this paper we provide a theoretical analysis of counterfactual invariance.
We present a variety of existing definitions, study how they relate to each
other and what their graphical implications are. We then turn to the current
major question surrounding counterfactual invariance, how does it relate to
conditional independence? We show that whilst counterfactual invariance implies
conditional independence, conditional independence does not give any
implications about the degree or likelihood of satisfying counterfactual
invariance. Furthermore, we show that for discrete causal models
counterfactually invariant functions are often constrained to be functions of
particular variables, or even constant.

本文从理论角度分析了反事实不变性的各种定义及其相关性，包括条件独立性是否能证明其强弱程度和可能性。 针对离散因果模型，我们证明了反事实不变函数通常只能是特定变量的函数，甚至是常数。

反事实不变性的结果

Results on Counterfactual Invariance

Informally, a 'spurious correlation' is the dependence of a model on some
aspect of the input data that an analyst thinks shouldn't matter. In machine
learning, these have a know-it-when-you-see-it character; e.g., changing the
gender of a sentence's subject changes a sentiment predictor's output. To check
for spurious correlations, we can 'stress test' models by perturbing irrelevant
parts of input data and seeing if model predictions change. In this paper, we
study stress testing using the tools of causal inference. We introduce
counterfactual invariance as a formalization of the requirement that changing
irrelevant parts of the input shouldn't change model predictions. We connect
counterfactual invariance to out-of-domain model performance, and provide
practical schemes for learning (approximately) counterfactual invariant
predictors (without access to counterfactual examples). It turns out that both
the means and implications of counterfactual invariance depend fundamentally on
the true underlying causal structure of the data -- in particular, whether the
label causes the features or the features cause the label. Distinct causal
structures require distinct regularization schemes to induce counterfactual
invariance. Similarly, counterfactual invariance implies different domain shift
guarantees depending on the underlying causal structure. This theory is
supported by empirical results on text classification.

本文通过对原因推断的工具进行研究，介绍了反事实不变性作为对无关输入部分进行更改时不应改变模型预测的要求的一个形式化。同时，提供了学习（近似）反事实不变预测器的实用方案，并对文本分类进行了实证研究。