Related papers: Inferring the finest pattern of mutual independenc…
A new method to measure nonlinear dependence between two variables is described using mutual information to analyze the separate linear and nonlinear components of dependence. This technique, which gives an exact value for the proportion of…
The beta model is the most important distribution for fitting data with the unit interval. However, the beta distribution is not suitable to model bimodal unit interval data. In this paper, we propose a bimodal beta distribution constructed…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
Neural networks are ubiquitous in many tasks, but trusting their predictions is an open issue. Uncertainty quantification is required for many applications, and disentangled aleatoric and epistemic uncertainties are best. In this paper, we…
This paper discusses the statistical inference problem associated with testing for dependence between two continuous random variables using Kendall's $\tau$ in the context of the missing data problem. We prove the worst-case identified set…
Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent.…
In this paper, the maximal nonlinear conditional correlation of two random vectors $X$ and $Y$ given another random vector $Z$, denoted by $\rho_1(X,Y|Z)$, is defined as a measure of conditional association, which satisfies certain…
We study the asymptotic behavior of the marginal expected shortfall when the two random variables are asymptotic independent but positive associated, which is modeled by the so-called tail dependent coefficient. We construct an estimator of…
The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…
Extremal dependence describes the strength of correlation between the largest observations of two variables. It is usually measured with symmetric dependence coefficients that do not depend on the order of the variables. In many cases,…
This paper aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we…
Statistical dependence measures like mutual information is ideal for analyzing autoencoders, but it can be ill-posed for deterministic, static, noise-free networks. We adopt the variational (Gaussian) formulation that makes dependence among…
A common approach to synthetic data is to sample from a fitted model. We show that under general assumptions, this approach results in a sample with inefficient estimators and whose joint distribution is inconsistent with the true…
The model-X conditional randomization test is a generic framework for conditional independence testing, unlocking new possibilities to discover features that are conditionally associated with a response of interest while controlling type-I…
We propose a general new method, the conditional permutation test, for testing the conditional independence of variables $X$ and $Y$ given a potentially high-dimensional random vector $Z$ that may contain confounding factors. The proposed…
The XGamma distribution is a generated distribution from a mixture of Exponential and Gamma distributions. It is found that in many cases the XGamma has more flexibility than the Exponential distribution. In this paper we consider the sum…
We present a model-free data-driven inference method that enables inferences on system outcomes to be derived directly from empirical data without the need for intervening modeling of any type, be it modeling of a material law or modeling…
Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the…
Let $\Lambda$ be the collection of all probability distributions for $(X,\widetilde{X})$, where $X$ is a fixed random vector and $\widetilde{X}$ ranges over all possible knockoff copies of $X$ (in the sense of \cite{CFJL18}). Three topics…
Two families of dependence measures between random variables are introduced. They are based on the R\'enyi divergence of order $\alpha$ and the relative $\alpha$-entropy, respectively, and both dependence measures reduce to Shannon's mutual…