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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…
Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take…
Conditional independence (CI) testing is a fundamental task in modern statistics and machine learning. The conditional randomization test (CRT) was recently introduced to test whether two random variables, $X$ and $Y$, are conditionally…
Nonparametric and nonlinear measures of statistical dependence between pairs of random variables are important tools in modern data analysis. In particular the emergence of large data sets can now support the relaxation of linearity…
Our evolution as a species made a huge step forward when we understood the relationships between causes and effects. These associations may be trivial for some events, but they are not in complex scenarios. To rigorously prove that some…
Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence…
Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the…
The PC algorithm is the state-of-the-art algorithm for causal structure discovery on observational data. It can be computationally expensive in the worst case due to the conditional independence tests are performed in an…
In this paper, our interest is in the problem of simultaneous hypothesis testing when the test statistics corresponding to the individual hypotheses are possibly correlated. Specifically, we consider the case when the test statistics…
We consider nonparametric sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution with some loose constraints. We…
This paper develops a model-free sequential test for conditional independence. The proposed test allows researchers to analyze an incoming i.i.d. data stream with any arbitrary dependency structure, and safely conclude whether a feature is…
Conditional independence tests (CI tests) have received special attention lately in Machine Learning and Computational Intelligence related literature as an important indicator of the relationship among the variables used by their models.…
We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional…
In recent years, many methods have been developed for detecting causal relationships in observational data. Some of them have the potential to tackle large data sets. However, these methods fail to discover a combined cause, i.e. a…
We give a new consistent scoring function for structure learning of Bayesian networks. In contrast to traditional approaches to score-based structure learning, such as BDeu or MDL, the complexity penalty that we propose is data-dependent…
Scientists regularly pose questions about treatment effects on outcomes conditional on a post-treatment event. However, causal inference in such settings requires care, even in perfectly executed randomized experiments. Recently, the…
In this paper, we study a generalization of the two-groups model in the presence of covariates --- a problem that has recently received much attention in the statistical literature due to its applicability in multiple hypotheses testing…
Causal discovery aims to recover causal structures or models underlying the observed data. Despite its success in certain domains, most existing methods focus on causal relations between observed variables, while in many scenarios the…
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…
Causal effect estimation from observational data is a challenging problem, especially with high dimensional data and in the presence of unobserved variables. The available data-driven methods for tackling the problem either provide an…