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Causal discovery from data affected by unobserved variables is an important but difficult problem to solve. The effects that unobserved variables have on the relationships between observed variables are more complex in nonlinear cases than…

Machine Learning · Computer Science 2021-06-07 Takashi Nicholas Maeda , Shohei Shimizu

Comparing counterfactual distributions can provide more nuanced and valuable measures for causal effects, going beyond typical summary statistics such as averages. In this work, we consider characterizing causal effects via distributional…

Machine Learning · Statistics 2024-11-05 Kwangho Kim , Jisu Kim , Edward H. Kennedy

The discovery of causal relationships from purely observational data is a fundamental problem in science. The most elementary form of such a causal discovery problem is to decide whether X causes Y or, alternatively, Y causes X, given joint…

Machine Learning · Computer Science 2016-05-03 Joris M. Mooij , Jonas Peters , Dominik Janzing , Jakob Zscheischler , Bernhard Schölkopf

Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric…

Causal inference is capable of estimating the treatment effect (i.e., the causal effect of treatment on the outcome) to benefit the decision making in various domains. One fundamental challenge in this research is that the treatment…

Machine Learning · Computer Science 2021-12-28 Qian Li , Zhichao Wang , Shaowu Liu , Gang Li , Guandong Xu

Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…

Machine Learning · Computer Science 2023-05-29 Yingtao Luo , Qiang Liu , Yuntian Chen , Wenbo Hu , Tian Tian , Jun Zhu

A predictive model makes outcome predictions based on some given features, i.e., it estimates the conditional probability of the outcome given a feature vector. In general, a predictive model cannot estimate the causal effect of a feature…

Machine Learning · Computer Science 2023-04-11 Jiuyong Li , Lin Liu , Ziqi Xu , Ha Xuan Tran , Thuc Duy Le , Jixue Liu

Causal inference is best understood using potential outcomes. This use is particularly important in more complex settings, that is, observational studies or randomized experiments with complications such as noncompliance. The topic of this…

Statistics Theory · Mathematics 2007-06-13 Donald B. Rubin

Quantum mechanics gives a new breakthrough to the field of parameter estimation. In the realm of quantum metrology, the precision of parameter estimation is limited by the quantum Fisher information. We introduce the measures of partial…

Quantum Physics · Physics 2024-11-14 Dong-Ping Xuan , Zhong-Xi Shen , Wen Zhou , Hua Nan , Shao-Ming Fei , Zhi-Xi Wang

In this paper we study the problems of estimating heterogeneity in causal effects in experimental or observational studies and conducting inference about the magnitude of the differences in treatment effects across subsets of the…

Machine Learning · Statistics 2022-06-08 Susan Athey , Guido Imbens

Area-specific causal inference is important in many policy and survey applications, where the goal is to evaluate treatment effects for small geographic or demographic domains. Existing causal small area estimation methods, however,…

Statistics Theory · Mathematics 2026-05-06 Tsubasa Ito , Shonosuke Sugasawa

Additive noise models (ANMs) are an important setting studied in causal inference. Most of the existing works on ANMs assume causal sufficiency, i.e., there are no unobserved confounders. This paper focuses on confounded ANMs, where a set…

Methodology · Statistics 2024-07-16 Muhammad Qasim Elahi , Mahsa Ghasemi , Murat Kocaoglu

A further understanding of cause and effect within observational data is critical across many domains, such as economics, health care, public policy, web mining, online advertising, and marketing campaigns. Although significant advances…

Machine Learning · Computer Science 2023-04-11 Zhixuan Chu , Sheng Li

In this paper, we introduce a new causal methodology that accounts for the rarity and frequency of events in observational studies based on their relevance to the underlying problem. Specifically, we propose a direct causal effect metric…

Artificial Intelligence · Computer Science 2025-02-28 Usef Faghihi , Amir Saki

The notion of causal effect is fundamental across many scientific disciplines. Traditionally, quantitative researchers have studied causal effects at the level of variables; for example, how a certain drug dose (W) causally affects a…

Methodology · Statistics 2026-04-07 Junhyung Park , Yuqing Zhou

Reasoning based on causality, instead of association has been considered as a key ingredient towards real machine intelligence. However, it is a challenging task to infer causal relationship/structure among variables. In recent years, an…

Machine Learning · Computer Science 2019-09-15 Zhitang Chen , Shengyu Zhu , Yue Liu , Tim Tse

In some causal inference scenarios, the treatment variable is measured inaccurately, for instance in epidemiology or econometrics. Failure to correct for the effect of this measurement error can lead to biased causal effect estimates.…

Machine Learning · Computer Science 2024-09-13 Antti Pöllänen , Pekka Marttinen

Single-parameter summaries of variable effects in regression settings are desirable for ease of interpretation. However (partially) linear models for example, which would deliver these, may fit poorly to the data. On the other hand, an…

Statistics Theory · Mathematics 2025-07-28 Harvey Klyne , Rajen D. Shah

This study demonstrates the existence of a testable condition for the identification of the causal effect of a treatment on an outcome in observational data, which relies on two sets of variables: observed covariates to be controlled for…

Econometrics · Economics 2026-05-20 Martin Huber , Jannis Kueck

When the causal relationship between X and Y is specified by a structural equation, the causal effect of X on Y is the expected rate of change of Y with respect to changes in X, when all other variables are kept fixed. This causal effect is…

Statistics Theory · Mathematics 2021-05-13 Wing Hung Wong