We study the problem of learning causal models from observational data through the lens of interpolation and its counterpart -- regularization. A large volume of recent theoretical, as well as empirical work, suggests that, in highly complex model classes, interpolating estimators can have good statistical generalization properties and can even be optimal for statistical learning. Motivated by an analogy between statistical and causal learning recently highlighted by Janzing (2019), we investigate whether interpolating estimators can also learn good causal models. To this end, we consider a simple linearly confounded model and derive precise asymptotics for the *causal risk* of the min-norm interpolator and ridge-regularized regressors in the high-dimensional regime. Under the principle of independent causal mechanisms, a standard assumption in causal learning, we find that interpolators cannot be optimal and causal learning requires stronger regularization than statistical learning. This resolves a recent conjecture in Janzing (2019). Beyond this assumption, we find a larger range of behavior that can be precisely characterized with a new measure of *confounding strength*. If the confounding strength is negative, causal learning requires weaker regularization than statistical learning, interpolators can be optimal, and the optimal regularization can even be negative. If the confounding strength is large, the optimal regularization is infinite, and learning from observational data is actively harmful.
Coarse-to-Fine Learning of Dynamic Causal Structures
School of Software（软件学院）；Shandong University（山东大学）；Department of Computer Science（计算机科学系）；New York University（纽约大学）；George Mason University（乔治·马歇尔大学）；Shandong Institutes of Industrial Technology（山东省工业技术研究院）
A Gradient-based Causal Discovery Framework with Applications to Complex Industrial Processes
School of Artificial Intelligence, Beijing Normal University（北京师范大学人工智能学院）；Advanced Institute of Natural Sciences, Beijing Normal University（北京师范大学自然科学院）
Optimistic Rates: A Unifying Theory for Interpolation Learning and Regularization in Linear Regression
University of Chicago（芝加哥大学）；Simons Institute, University of California at Berkeley（加州大学伯克利分校西蒙斯研究所）；University of British Columbia（不列颠哥伦比亚大学）；Alberta Machine Intelligence Institute（阿尔伯塔机器智能研究所）；Toyota Technological Institute at Chicago（芝加哥丰田技术研究所）
我们研究了高斯数据线性回归的一致收敛的局部概念，称为“乐观率”（Panchenko 2002; Srebro et al. 2010）。我们的精细分析避免了现有结果中的隐藏常数和对数因子，这些因子在高维环境中至关重要，特别是对于理解插值学习。作为一种特殊情况，我们的分析恢复了Koehler et al.（2021）的保证，该保证严格描述了良性过拟合条件下低范数插值器的总体风险。然而，我们的乐观率界也分析了具有任意训练误差的预测器。这使我们能够恢复一些经典的随机设计下的岭和LASSO回归的统计保证，并帮助我们获得一个精确的理解过度参数化制度的过度风险的近插值。
Sinkhorn Treatment Effects: A Causal Optimal Transport Measure
Department of Statistics, University of Washington, Seattle, WA, USA（华盛顿大学统计学系）；Department of Health Care Policy, Harvard Medical School, Boston, MA, USA（哈佛医学院医疗政策系）
