One of the goals of causal inference is to generalize from past experiments and observational data to novel conditions. While it is in principle possible to eventually learn a mapping from a novel experimental condition to an outcome of interest, provided a sufficient variety of experiments is available in the training data, coping with a large combinatorial space of possible interventions is hard. Under a typical sparse experimental design, this mapping is ill-posed without relying on heavy regularization or prior distributions. Such assumptions may or may not be reliable, and can be hard to defend or test. In this paper, we take a close look at how to warrant a leap from past experiments to novel conditions based on minimal assumptions about the factorization of the distribution of the manipulated system, communicated in the well-understood language of factor graph models. A postulated $\textit{interventional factor model}$ (IFM) may not always be informative, but it conveniently abstracts away a need for explicitly modeling unmeasured confounding and feedback mechanisms, leading to directly testable claims. Given an IFM and datasets from a collection of experimental regimes, we derive conditions for identifiability of the expected outcomes of new regimes never observed in these training data. We implement our framework using several efficient algorithms, and apply them on a range of semi-synthetic experiments.
Identification Methods With Arbitrary Interventional Distributions as Inputs
Johns Hopkins University（约翰斯·霍普金斯大学）
因果推断通过估计数据中的反事实参数来量化因果关系。这需要使用\emph{identification theory}在感兴趣的反事实参数和数据可用的分布之间建立联系。一系列工作的特点是非参数识别的各种因果参数的\emph{observed data distribution}。最近，识别结果已扩展到设置中的实验数据从干预分布也是可用的。在本文中，我们使用单世界干预图和嵌套因式分解的模型与混合图给出了一个非常简单的视图，现有的识别理论的实验数据。我们使用这种观点来产生一般的识别算法的设置，其中输入分布包括一组任意的观测和实验分布，包括边际和条件分布。我们表明，对于问题的输入是干预边缘分布的某种类型（祖先边缘），我们的算法是完整的。
Scalable Contrastive Causal Discovery under Unknown Soft Interventions
Department of Systems Biology, Columbia University Irving Institute for Cancer Dynamics, Columbia University（系统生物学系，哥伦比亚大学伊万尼癌症动力学研究所，哥伦比亚大学）；Irving Institute for Cancer Dynamics, Columbia University（伊万尼癌症动力学研究所，哥伦比亚大学）；Department of Computer Science, Columbia University（计算机科学系，哥伦比亚大学）；Department of Biomedical Engineering, Columbia University（生物医学工程系，哥伦比亚大学）；Data Science Institute, Columbia University（数据科学研究所，哥伦比亚大学）
我们推导出上界的泛化误差的学习算法的基础上，他们的\emph{algorithmic transport cost}：预期的瓦瑟斯坦距离之间的输出假设和输出假设的输入示例为条件。边界提供了一种新的方法来研究学习算法的推广，从最优传输的观点，并施加更少的限制，如亚高斯或有界的损失函数。我们进一步提供了几个上界的算法运输成本的全变差距离，相对熵（或KL发散），和VC维，从而进一步桥接最优运输理论和信息理论与统计学习理论。此外，我们还研究了损失函数的不同条件下，学习算法的泛化误差可以由不同的概率距离分布之间的上限与输出假设和/或输入数据。最后，在我们建立的框架下，我们分析了深度学习中的泛化，并得出结论，随着层数的增加，深度神经网络（DNN）中的泛化误差呈指数下降到零。我们对深度学习泛化错误的分析主要利用了DNN的层次结构和$f$ -发散的收缩特性，这可能对分析其他具有层次结构的学习模型具有独立的意义。
