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The algorithmic Markov condition states that the most likely causal direction between two random variables X and Y can be identified as that direction with the lowest Kolmogorov complexity. Due to the halting problem, however, this notion…

Machine Learning · Computer Science 2017-02-23 Kailash Budhathoki , Jilles Vreeken

We consider the fundamental problem of inferring the causal direction between two univariate numeric random variables $X$ and $Y$ from observational data. The two-variable case is especially difficult to solve since it is not possible to…

Machine Learning · Statistics 2018-08-23 Alexander Marx , Jilles Vreeken

Given data over the joint distribution of two random variables $X$ and $Y$, we consider the problem of inferring the most likely causal direction between $X$ and $Y$. In particular, we consider the general case where both $X$ and $Y$ may be…

Machine Learning · Statistics 2017-10-17 Alexander Marx , Jilles Vreeken

The algorithmic independence of conditionals, which postulates that the causal mechanism is algorithmically independent of the cause, has recently inspired many highly successful approaches to distinguish cause from effect given only…

Information Theory · Computer Science 2021-05-06 Alexander Marx , Jilles Vreeken

Bivariate causal direction identification is a fundamental and vital problem in the causal inference field. Among binary causal methods, most methods based on additive noise only use one single causal mechanism to construct a causal model.…

Artificial Intelligence · Computer Science 2025-07-30 Saixiong Liu , Yuhua Qian , Jue Li , Honghong Cheng , Feijiang Li

Inferring the causal structure that links n observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when only…

Statistics Theory · Mathematics 2008-04-24 Dominik Janzing , Bernhard Schoelkopf

Approaches to bivariate causal discovery based on the minimum description length (MDL) principle approximate the (uncomputable) Kolmogorov complexity of the models in each causal direction, selecting the one with the lower total complexity.…

Machine Learning · Computer Science 2026-04-08 Tiago Brogueira , Mário A. T. Figueiredo

We summarize our recent findings, where we proposed a framework for learning a Kolmogorov model, for a collection of binary random variables. More specifically, we derive conditions that link outcomes of specific random variables, and…

Machine Learning · Computer Science 2018-06-07 Hadi Ghauch , Mikael Skoglund , Hossein Shokri-Ghadikolaei , Carlo Fischione , Ali H. Sayed

The causal Markov condition (CMC) is a postulate that links observations to causality. It describes the conditional independences among the observations that are entailed by a causal hypothesis in terms of a directed acyclic graph. In the…

Information Theory · Computer Science 2010-02-23 Bastian Steudel , Dominik Janzing , Bernhard Schoelkopf

Causal inference plays an important role in explanatory analysis and decision making across various fields like statistics, marketing, health care, and education. Its main task is to estimate treatment effects and make intervention…

Methodology · Statistics 2024-07-22 Yingrong Wang , Haoxuan Li , Minqin Zhu , Anpeng Wu , Ruoxuan Xiong , Fei Wu , Kun Kuang

Telling apart the cause and effect between two random variables with purely observational data is a challenging problem that finds applications in various scientific disciplines. A key principle utilized in this task is the algorithmic…

Machine Learning · Computer Science 2025-08-15 Quang-Duy Tran , Bao Duong , Phuoc Nguyen , Thin Nguyen

Causal inference has been a pivotal challenge across diverse domains such as medicine and economics, demanding a complicated integration of human knowledge, mathematical reasoning, and data mining capabilities. Recent advancements in…

Computation and Language · Computer Science 2025-02-11 Jing Ma

We develop methodology for causal inference in observational studies when using propensity score subclassification on data constructed with probabilistic record linkage techniques. We focus on scenarios where covariates and binary treatment…

Methodology · Statistics 2018-04-03 Joan Heck Wortman , Jerome P. Reiter

We address the problem of determining the causal direction between two univariate, continuous-valued variables, X and Y, under the assumption of no hidden confounders. In general, it is not possible to make definitive statements about…

Machine Learning · Statistics 2025-09-03 Katerina Hlavackova-Schindler , Suzana Marsela

Discovering the causal structure among a set of variables is a fundamental problem in many areas of science. In this paper, we propose Kernel Conditional Deviance for Causal Inference (KCDC) a fully nonparametric causal discovery method…

Machine Learning · Computer Science 2018-04-13 Jovana Mitrovic , Dino Sejdinovic , Yee Whye Teh

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing…

Methodology · Statistics 2020-02-10 Liuyi Yao , Zhixuan Chu , Sheng Li , Yaliang Li , Jing Gao , Aidong Zhang

Inferring causal relationships between variable pairs is crucial for understanding multivariate interactions in complex systems. Knowledge-based causal discovery -- which involves inferring causal relationships by reasoning over the…

Artificial Intelligence · Computer Science 2025-06-11 Yuni Susanti , Michael Färber

Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates,…

Artificial Intelligence · Computer Science 2026-02-17 Yuxuan Xie , Ang Li

The machine learning community has recently devoted much attention to the problem of inferring causal relationships from statistical data. Most of this work has focused on uncovering connections among scalar random variables. We generalize…

Machine Learning · Statistics 2012-07-10 Doris Entner , Patrik O. Hoyer

Classical machine learning techniques often struggle with overfitting and unreliable predictions when exposed to novel conditions. Introducing causality into the modelling process offers a promising way to mitigate these challenges by…

Computational Engineering, Finance, and Science · Computer Science 2025-05-28 David Zapata Gonzalez , Marcel Meyer , Oliver Mueller
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