Related papers: Nearest-Neighbor Sampling Based Conditional Indepe…
The conditional mutual information I(X;Y|Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model…
This paper introduces a new concept of stochastic dependence among many random variables which we call conditional neighborhood dependence (CND). Suppose that there are a set of random variables and a set of sigma algebras where both sets…
Conditional independence (CI) testing is frequently used in data analysis and machine learning for various scientific fields and it forms the basis of constraint-based causal discovery. Oftentimes, CI testing relies on strong, rather…
We propose two nonparametric statistical tests of goodness of fit for conditional distributions: given a conditional probability density function $p(y|x)$ and a joint sample, decide whether the sample is drawn from $p(y|x)r_x(x)$ for some…
(To appear in The American Statistician.) Distance covariance (Sz\'ekely, Rizzo, and Bakirov, 2007) is a fascinating recent notion, which is popular as a test for dependence of any type between random variables $X$ and $Y$. This approach…
Conditional specification of distributions is a developing area with increasing applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we propose an alternative approach to study the…
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data…
Consider a random sample $X_1 , X_2 , ..., X_n$ drawn independently and identically distributed from some known sampling distribution $P_X$. Let $X_{(1)} \le X_{(2)} \le ... \le X_{(n)}$ represent the order statistics of the sample. The…
The standard method to check for the independence of two real-valued random variables -- demonstrating that the bivariate joint distribution factors into the product of its marginals -- is both necessary and sufficient. Here we present a…
We introduce a new test for conditional independence which is based on what we call the weighted generalised covariance measure (WGCM). It is an extension of the recently introduced generalised covariance measure (GCM). To test the null…
Graph data has a unique structure that deviates from standard data assumptions, often necessitating modifications to existing methods or the development of new ones to ensure valid statistical analysis. In this paper, we explore the notion…
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…
This work addresses testing the independence of two continuous and finite-dimensional random variables from the design of a data-driven partition. The empirical log-likelihood statistic is adopted to approximate the sufficient statistics of…
This paper introduces a statistical test inferring whether a variable allows separating two classes by means of a single critical value. Its test statistic is the prediction error of a nonparametric threshold classifier. While this approach…
Consider a positive random variable of interest Y depending on a covariate X, and a random observation time T independent of Y given X. Assume that the only knowledge available about Y is its current status at time T: \delta = 1_{Y \leq T}.…
Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…
Separable Bayesian Networks, or the Influence Model, are dynamic Bayesian Networks in which the conditional probability distribution can be separated into a function of only the marginal distribution of a node's neighbors, instead of the…
In this article, we consider the problem of testing the independence between two random variables. Our primary objective is to develop tests that are highly effective at detecting associations arising from explicit or implicit functional…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
A coefficient is introduced that quantifies the extent of separation of a random variable $Y$ relative to a number of variables $\mathbf{X} = (X_1, \dots, X_p)$ by skillfully assessing the sensitivity of the relative effects of the…