Related papers: Covariate-adjusted statistical dependence represen…
Dependence strucuture estimation is one of the important problems in machine learning domain and has many applications in different scientific areas. In this paper, a theoretical framework for such estimation based on copula and copula…
Vine copulas are a flexible tool for multivariate non-Gaussian distributions. For data from an observational study where the explanatory variables and response variables are measured together, a proposed vine copula regression method uses…
Verification and validation of fully automated vehicles is linked to an almost intractable challenge of reflecting the real world with all its interactions in a virtual environment. Influential stochastic parameters need to be extracted…
In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…
Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…
Study of recurrences in earthquakes, climate, financial time-series, etc. is crucial to better forecast disasters and limit their consequences. However, almost all the previous phenomenological studies involved only a long-ranged…
Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of…
Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates,…
The empirical copula process plays a central role for statistical inference on copulas. Recently, Segers (2011) investigated the asymptotic behavior of this process under non-restrictive smoothness assumptions for the case of i.i.d. random…
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…
In this paper, we derive copula-based and empirical dependency models (DMs) for simulating non-independent variables, and then propose a new way for determining the distribution of the model outputs conditional on every subset of inputs.…
Studying the multivariate extension of copula correlation yields a dimension reduction principle, which turns out to be strongly related with the `simple measure of conditional dependence' $T$ recently introduced by Azadkia & Chatterjee…
Multivariate mixed-type outcomes are difficult to model jointly, and additional complexity arises when both marginal effects and dependence structures vary with a covariate such as age or time. Existing approaches often impose restrictive…
High-dimensional covariates often admit linear factor structure. To effectively screen correlated covariates in high-dimension, we propose a conditional variable screening test based on non-parametric regression using neural networks due to…
It is well known that the dependence structure for jointly Gaussian variables can be fully captured using correlations, and that the conditional dependence structure in the same way can be described using partial correlations. The partial…
Inference of the conditional dependence structure is challenging when many covariates are present. In numerous applications, only a low-dimensional projection of the covariates influences the conditional distribution. The smallest subspace…
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…
Based on recent progress in research on copula based dependence measures, we review the original Renyi's axioms on symmetric measures and propose a new set of axioms that applies to nonsymmetric measures. We show that nonsymmetric measures…
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…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…