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Related papers: On the Hardness of Conditional Independence Testin…

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We investigate the problem of testing whether $d$ random variables, which may or may not be continuous, are jointly (or mutually) independent. Our method builds on ideas of the two variable Hilbert-Schmidt independence criterion (HSIC) but…

Statistics Theory · Mathematics 2016-11-07 Niklas Pfister , Peter Bühlmann , Bernhard Schölkopf , Jonas Peters

Given independent samples generated from the joint distribution $p(\mathbf{x},\mathbf{y},\mathbf{z})$, we study the problem of Conditional Independence (CI-Testing), i.e., whether the joint equals the CI distribution…

Machine Learning · Statistics 2018-06-27 Rajat Sen , Karthikeyan Shanmugam , Himanshu Asnani , Arman Rahimzamani , Sreeram Kannan

In this paper we provide a theoretical analysis of counterfactual invariance. We present a variety of existing definitions, study how they relate to each other and what their graphical implications are. We then turn to the current major…

Machine Learning · Computer Science 2023-07-18 Jake Fawkes , Robin J. Evans

Conditional randomization tests (CRTs) assess whether a variable $x$ is predictive of another variable $y$, having observed covariates $z$. CRTs require fitting a large number of predictive models, which is often computationally…

Methodology · Statistics 2023-04-12 Mukund Sudarshan , Aahlad Manas Puli , Wesley Tansey , Rajesh Ranganath

We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…

Methodology · Statistics 2026-01-28 Jinyuan Chang , Yue Du , Jing He , Qiwei Yao

It is well-known that the notion of (strong) conditional independence (CI) is too restrictive to capture independencies that only hold in certain contexts. This kind of contextual independency, called context-strong independence (CSI), can…

Artificial Intelligence · Computer Science 2013-01-30 Michael S. K. M. Wong , C. J. Butz

We introduce a kernel-based goodness-of-fit test for censored data, where observations may be missing in random time intervals: a common occurrence in clinical trials and industrial life-testing. The test statistic is straightforward to…

Methodology · Statistics 2018-10-11 Tamara Fernández , Arthur Gretton

A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the…

Machine Learning · Statistics 2016-10-18 Wittawat Jitkrittum , Zoltan Szabo , Arthur Gretton

In real supervised learning scenarios, it is not uncommon that the training and test sample follow different probability distributions, thus rendering the necessity to correct the sampling bias. Focusing on a particular covariate shift…

Machine Learning · Computer Science 2012-06-22 Yaoliang Yu , Csaba Szepesvari

Dependence measures based on reproducing kernel Hilbert spaces, also known as Hilbert-Schmidt Independence Criterion and denoted HSIC, are widely used to statistically decide whether or not two random vectors are dependent. Recently,…

Statistics Theory · Mathematics 2021-01-13 Mélisande Albert , Béatrice Laurent , Amandine Marrel , Anouar Meynaoui

A statistical test of independence may be constructed using the Hilbert-Schmidt Independence Criterion (HSIC) as a test statistic. The HSIC is defined as the distance between the embedding of the joint distribution, and the embedding of the…

Machine Learning · Statistics 2015-01-27 Arthur Gretton

Representations of probability measures in reproducing kernel Hilbert spaces provide a flexible framework for fully nonparametric hypothesis tests of independence, which can capture any type of departure from independence, including…

Computation · Statistics 2018-06-11 Qinyi Zhang , Sarah Filippi , Arthur Gretton , Dino Sejdinovic

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

We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…

Methodology · Statistics 2025-10-29 Jian Yan , Zhuoxi Li , Yang Ning , Yong Chen

The average treatment effect, which is the difference in expectation of the counterfactuals, is probably the most popular target effect in causal inference with binary treatments. However, treatments may have effects beyond the mean, for…

Methodology · Statistics 2023-11-02 Diego Martinez-Taboada , Aaditya Ramdas , Edward H. Kennedy

Testing hypothesis of independence between two random elements on a joint alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is an effective test for such a situation when the contingency table is relatively small.…

Statistics Theory · Mathematics 2025-03-19 Jialin Zhang , Zhiyi Zhang

Many unsupervised kernel methods rely on the estimation of the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). Both kernel CO and kernel CCO are sensitive to contaminated data, even when bounded…

Machine Learning · Statistics 2017-05-12 Md. Ashad Alam , Kenji Fukumizu , Yu-Ping Wang

We study a class of determinantal ideals that are related to conditional independence (CI) statements with hidden variables. Such CI statements correspond to determinantal conditions on a matrix whose entries are probabilities of events…

Commutative Algebra · Mathematics 2023-01-02 Oliver Clarke , Fatemeh Mohammadi , Johannes Rauh

Testing the dependency between two random variables is an important inference problem in statistics since many statistical procedures rely on the assumption that the two samples are independent. To test whether two samples are independent,…

Methodology · Statistics 2023-01-04 Jin-Ting Zhang , Tianming Zhu

We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables $(A, B, C)$ with unknown…

Data Structures and Algorithms · Computer Science 2025-06-05 Jan Seyfried , Sayantan Sen , Marco Tomamichel