Advancing Counterfactual Inference through Nonlinear Quantile Regression
Carnegie Mellon University（卡内基梅隆大学）；University of California San Diego（加利福尼亚大学圣迭戈分校）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；The University of Sydney（悉尼大学）
Shaoan Xie, Biwei Huang, Bin Gu, Tongliang Liu, Kun Zhang
回答反事实“如果……会怎样”问题的能力，对于理解和利用因果影响至关重要。在 Pearl 的反事实框架下，传统反事实推断通常依赖于能够获取或估计一个结构因果模型。然而在实践中，该因果模型往往未知，并且可能难以识别。因此，本文旨在仅基于观测数据和（学习到的）定性因果结构开展可靠的反事实推断，而无需预定义因果模型，甚至无需直接估计条件分布。为此，我们建立了反事实推断与分位数回归之间的一种新联系，并证明反事实推断可以被重新表述为一个扩展的分位数回归问题。基于这一洞见，我们提出了一个实用框架，用于在双层优化方案下利用神经网络实现高效且有效的反事实推断。所提方法增强了将估计的反事实结果泛化到未见数据的能力，从而给出了泛化误差的上界。此外，实证证据表明，与现有方法相比，其具有更优的统计效率。在多个数据集上进行的实证结果为我们的理论论断提供了有力支持。
英文摘要：
The capacity to address counterfactual "what if" inquiries is crucial for understanding and making use of causal influences. Traditional counterfactual inference, under Pearls' counterfactual framework, typically depends on having access to or estimating a structural causal model. Yet, in practice, this causal model is often unknown and might be challenging to identify. Hence, this paper aims to perform reliable counterfactual inference based solely on observational data and the (learned) qualitative causal structure, without necessitating a predefined causal model or even direct estimations of conditional distributions. To this end, we establish a novel connection between counterfactual inference and quantile regression and show that counterfactual inference can be reframed as an extended quantile regression problem. Building on this insight, we propose a practical framework for efficient and effective counterfactual inference implemented with neural networks under a bi-level optimization scheme. The proposed approach enhances the capacity to generalize estimated counterfactual outcomes to unseen data, thereby providing an upper bound on the generalization error. Furthermore, empirical evidence demonstrates its superior statistical efficiency in comparison to existing methods. Empirical results conducted on multiple datasets offer compelling support for our theoretical assertions.
This article extends the widely-used synthetic controls estimator for evaluating causal effects of policy changes to quantile functions. The proposed method provides a geometrically faithful estimate of the entire counterfactual quantile function of the treated unit. Its appeal stems from an efficient implementation via a constrained quantile-on-quantile regression. This constitutes a novel concept of independent interest. The method provides a unique counterfactual quantile function in any scenario: for continuous, discrete or mixed distributions. It operates in both repeated cross-sections a…
Fairness of classification and regression has received much attention recently and various, partially non-compatible, criteria have been proposed. The fairness criteria can be enforced for a given classifier or, alternatively, the data can be adapated to ensure that every classifier trained on the data will adhere to desired fairness criteria. We present a practical data adaption method based on quantile preservation in causal structural equation models. The data adaptation is based on a presumed counterfactual model for the data. While the counterfactual model itself cannot be verified experi…
Standard causal inference characterizes treatment effect through averages, but the counterfactual distributions could be different in not only the central tendency but also spread and shape. To provide a comprehensive evaluation of treatment effects, we focus on estimating quantile treatment effects (QTEs). Existing methods that invert a nonsmooth estimator of the cumulative distribution functions forbid inference on probability density functions (PDFs), but PDFs can reveal more nuanced characteristics of the counterfactual distributions. We adopt a semiparametric conditional distribution regr…
This paper concerns estimation and inference for treatment effects in deep tails of the counterfactual distribution of unobservable potential outcomes corresponding to a continuously valued treatment. We consider two measures for the deep tail characteristics: the extreme quantile function and the tail mean function defined as the conditional mean beyond a quantile level. Then we define the extreme quantile treatment effect (EQTE) and the extreme average treatment effect (EATE), which can be identified through the commonly adopted unconfoundedness condition and estimated with the aid of extrem…
What is a good matching of probability measures? A counterfactual lens on transport maps
Institut Elie Cartan de Lorraine, Université de Lorraine（伊莱·卡坦研究所（洛林）、洛林大学）；Université Paris-Saclay, CNRS, Inria, Laboratoire de mathématiques d’Orsay（巴黎-萨克雷大学、国家科学研究中心、法国国家信息与自动化技术研究院、奥赛数学实验室）
Evaluating treatment effect heterogeneity widely informs treatment decision making. At the moment, much emphasis is placed on the estimation of the conditional average treatment effect via flexible machine learning algorithms. While these methods enjoy some theoretical appeal in terms of consistency and convergence rates, they generally perform poorly in terms of uncertainty quantification. This is troubling since assessing risk is crucial for reliable decision-making in sensitive and uncertain environments. In this work, we propose a conformal inference-based approach that can produce reliabl…
Flow Matching with In-Context Priors for Out-of-Distribution Brain Dynamics
Hertie Institute for AI in Brain Health, University of Tübingen（赫蒂人工智能脑健康研究所，图宾根大学）；Tübingen AI Center, University of Tübingen（图宾根人工智能中心，图宾根大学）；Charité – Universitätsmedizin Berlin, Department of Psychiatry and Psychotherapy（柏林夏里特医学院，精神病学与心理治疗系）；German Center for Mental Health (DZPG), partner site Tübingen（德国心理健康中心（DZPG），图宾根合作站点）
Extended Wasserstein-GAN Approach to Causal Distribution Learning: Density-Free Estimation and Minimax Optimality
The University of Tokyo（东京大学）；Japan Institute for Health Security（日本健康安全研究所）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进情报项目）；Kyoto University（京都大学）
Sun Yat-sen University（中山大学）；School of Public Health（公共卫生学院）
This dissertation focuses on modern causal inference under uncertainty and data restrictions, with applications to neoadjuvant clinical trials, distributed data networks, and robust individualized decision making. In the first project, we propose a method under the principal stratification framework to identify and estimate the average treatment effects on a binary outcome, conditional on the counterfactual status of a post-treatment intermediate response. Under mild assumptions, the treatment effect of interest can be identified. We extend the approach to address censored outcome data. The pr…
Shape restrictions have played a central role in economics as both testable implications of theory and sufficient conditions for obtaining informative counterfactual predictions. In this paper we provide a general procedure for inference under shape restrictions in identified and partially identified models defined by conditional moment restrictions. Our test statistics and proposed inference methods are based on the minimum of the generalized method of moments (GMM) objective function with and without shape restrictions. Uniformly valid critical values are obtained through a bootstrap procedu…
EvoMorph: Counterfactual Explanations for Continuous Time-Series Extrinsic Regression Applied to Photoplethysmography
Centre for Digital Health Interventions, ETH Zurich（数字健康干预中心，苏黎世联邦理工学院）；Centre for Digital Health Interventions, University of St.Gallen（数字健康干预中心，圣加伦大学）
