Related papers: On (Anti)Conditional Independence in Dempster-Shaf…

Shapley values have become one of the go-to methods to explain complex models to end-users. They provide a model agnostic post-hoc explanation with foundations in game theory: what is the worth of a player (in machine learning, a feature…

The asymptotic tail behaviour of sums of independent subexponential random variables is well understood, one of the main characteristics being the principle of the single big jump. We study the case of dependent subexponential random…

A celebrated theorem of Fr\"oberg gives a complete combinatorial classification of quadratic square-free monomial ideals with a linear resolution. A generalization of this theorem to higher degree square-free monomial ideals is an active…

We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…

We consider closure properties in the class of positively decreasing distributions. Our results stem from different types of dependence, but each type belongs in the family of asymptotically independent dependence structure. Namely we…

The Gaussian model equips strong properties that facilitate studying and interpreting graphical models. Specifically it reduces conditional independence and the study of positive association to determining partial correlations and their…

Absence of (complex) zeros property is at the heart of the interpolation method developed by Barvinok \cite{barvinok2017combinatorics} for designing deterministic approximation algorithms for various graph counting and computing partition…

In this work, we consider the maximization of submodular functions constrained by independence systems. Because of the wide applicability of submodular functions, this problem has been extensively studied in the literature, on specialized…

We introduce and study the property of orthogonal independence, a restricted additivity axiom applying when alternatives are orthogonal. The axiom requires that the preference for one marginal change over another should be maintained after…

We prove that the form of conditional independence at play in database theory and independence logic is reducible to the first-order dividing calculus in the theory of atomless Boolean algebras. This establishes interesting connections…

We propose a semantic foundation for logics for reasoning in settings that possess a distinction between equality of variables, a coarser equivalence of variables, and a notion of conditional independence between variables. We show that…

This paper establishes a complete theoretical foundation for the Hodge-theoretic extension of the Shapley value introduced by Stern and Tettenhorst (2019). We show that a set of five axioms--efficiency, linearity, symmetry, a modified…

It is a common saying that testing for conditional independence, i.e., testing whether whether two random vectors $X$ and $Y$ are independent, given $Z$, is a hard statistical problem if $Z$ is a continuous random variable (or vector). In…

In this paper, we derive a characterization theorem for the path-independent property of the density of the Girsanov transformation for {\it degenerated} stochastic differential equations (SDEs), extending the characterization theorem of…

We present a framework for studying the concept of independence in a general context covering database theory, algebra and model theory as special cases. We show that well-known axioms and rules of independence for making inferences…

In this paper we prove that decomposable forms, or homogeneous polynomials $F(x_1, \cdots, x_n)$ with integer coefficients which split completely into linear factors over $\mathbb{C}$, take on infinitely many square-free values subject to…

Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…

If for any $k$ the $k$-th coefficient of a polynomial I(G;x) is equal to the number of stable sets of cardinality $k$ in graph $G$, then it is called the independence polynomial of $G$ (Gutman and Harary, 1983). J. I. Brown, K. Dilcher and…

A primary motivation for reasoning under uncertainty is to derive decisions in the face of inconclusive evidence. However, Shafer's theory of belief functions, which explicitly represents the underconstrained nature of many reasoning…

We study properties of semi-elementary imsets and elementary imsets introduced by Studeny (2005). The rules of the semi-graphoid axiom (decomposition, weak union and contraction) for conditional independence statements can be translated…