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Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…

Independence screening is a powerful method for variable selection for `Big Data' when the number of variables is massive. Commonly used independence screening methods are based on marginal correlations or variations of it. In many…

We study the data-driven selection of causal graphical models using constraint-based algorithms, which determine the existence or non-existence of edges (causal connections) in a graph based on testing a series of conditional independence…

We investigate a class of methods for selective inference that condition on a selection event. Such methods follow a two-stage process. First, a data-driven (sub)collection of hypotheses is chosen from some large universe of hypotheses.…

Refining one's hypotheses in the light of data is a common scientific practice; however, the dependency on the data introduces selection bias and can lead to specious statistical analysis. An approach for addressing this is via conditioning…

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…

Intelligent test requires efficient and effective analysis of high-dimensional data in a large scale. Traditionally, the analysis is often conducted by human experts, but it is not scalable in the era of big data. To tackle this challenge,…

Bell inequalities may only be derived, if hidden variables do not depend on the experimental settings. The stochastic independence of hidden and setting variables is called: freedom of choice, free will, measurement independence or no…

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…

In this paper, we focus on the problem of stable prediction across unknown test data, where the test distribution is agnostic and might be totally different from the training one. In such a case, previous machine learning methods might…

Conditional independence testing is a key problem required by many machine learning and statistics tools. In particular, it is one way of evaluating the usefulness of some features on a supervised prediction problem. We propose a novel…

We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process…

Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is…

Variable selection comprises an important step in many modern statistical inference procedures. In the regression setting, when estimators cannot shrink irrelevant signals to zero, covariates without relationships to the response often…

Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables…

A common assumption in causal inference from observational data is that there is no hidden confounding. Yet it is, in general, impossible to verify this assumption from a single dataset. Under the assumption of independent causal mechanisms…

Estimating causal effects from observational data requires identifying valid adjustment sets. This task is especially challenging in realistic settings where latent confounding and feedback loops are present. Existing approaches typically…

Compositional data (i.e., data comprising random variables that sum up to a constant) arises in many applications including microbiome studies, chemical ecology, political science, and experimental designs. Yet when compositional data serve…

Conditioning on some set of confounders that causally affect both treatment and outcome variables can be sufficient for eliminating bias introduced by all such confounders when estimating causal effect of the treatment on the outcome from…

Genetical genomics experiments have now been routinely conducted to measure both the genetic markers and gene expression data on the same subjects. The gene expression levels are often treated as quantitative traits and are subject to…