Out-of-distribution (OOD) generalization is indispensable for learning models
in the wild, where testing distribution typically unknown and different from
the training. Recent methods derived from causality have shown great potential
in achieving OOD generalization. However, existing methods mainly focus on the
invariance property of causes, while largely overlooking the property of
\textit{sufficiency} and \textit{necessity} conditions. Namely, a necessary but
insufficient cause (feature) is invariant to distribution shift, yet it may not
have required accuracy. By contrast, a sufficient yet unnecessary cause
(feature) tends to fit specific data well but may have a risk of adapting to a
new domain. To capture the information of sufficient and necessary causes, we
employ a classical concept, the probability of sufficiency and necessary causes
(PNS), which indicates the probability of whether one is the necessary and
sufficient cause. To associate PNS with OOD generalization, we propose PNS risk
and formulate an algorithm to learn representation with a high PNS value. We
theoretically analyze and prove the generalizability of the PNS risk.
Experiments on both synthetic and real-world benchmarks demonstrate the
effectiveness of the proposed method. The details of the implementation can be
found at the GitHub repository: this https URL

通过应用概率的充分性和必要性概念 (PNS) 来提高模型的泛化能力，该方法在合成和真实基准测试中得到了验证。

通过充分和必要原因的概率进行不变性学习

Invariant Learning via Probability of Sufficient and Necessary Causes

Given a machine learning (ML) model and a prediction, explanations can be
defined as sets of features which are sufficient for the prediction. In some
applications, and besides asking for an explanation, it is also critical to
understand whether sensitive features can occur in some explanation, or whether
a non-interesting feature must occur in all explanations. This paper starts by
relating such queries respectively with the problems of relevancy and necessity
in logic-based abduction. The paper then proves membership and hardness results
for several families of ML classifiers. Afterwards the paper proposes concrete
algorithms for two classes of classifiers. The experimental results confirm the
scalability of the proposed algorithms.

该论文提出了解释机器学习模型预测的方法，同时讨论了相关性和必要性问题，证明了多个机器学习分类器的成员和困难性，并针对不同分类器提出了具体算法。实验结果表明所提算法的可扩展性较好。

机器学习分类器解释中特征的必要性和相关性

Feature Necessity & Relevancy in ML Classifier Explanations

Necessity and sufficiency are the building blocks of all successful
explanations. Yet despite their importance, these notions have been
conceptually underdeveloped and inconsistently applied in explainable
artificial intelligence (XAI), a fast-growing research area that is so far
lacking in firm theoretical foundations. Building on work in logic,
probability, and causality, we establish the central role of necessity and
sufficiency in XAI, unifying seemingly disparate methods in a single formal
framework. We provide a sound and complete algorithm for computing explanatory
factors with respect to a given context, and demonstrate its flexibility and
competitive performance against state of the art alternatives on various tasks.

在解释人工智能（XAI）这一快速发展的研究领域中，我们建立起必要性和充分性在 XAI 中的中心作用，通过逻辑、概率和因果关系的工作，将看似分散的方法统一到一个单一的形式框架中，并提供了一个可靠、完整的算法来计算与给定上下文相关的解释因素，展示了其灵活性和在各种任务上与最先进的替代方案的可比性。