Related papers: On (Anti)Conditional Independence in Dempster-Shaf…
Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests…
We study the free product of rooted graphs and its various decompositions using quantum probabilistic methods. We show that the free product of rooted graphs is canonically associated with free independence, which completes the proof of the…
We study classes of countable graphs where every member does not contain a given finite graph as an induced subgraph -- denoted by $\mathsf{Free}(\mathcal{G})$ for a given finite graph $\mathcal{G}$. Our main results establish a structural…
Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional…
The classes stable, simple and NSOP$_1$ in the stability hierarchy for first-order theories can be characterised by the existence of a certain independence relation. For each of them there is a canonicity theorem: there can be at most one…
The involution Stanley symmetric functions $\hat{F}_y$ are the stable limits of the analogues of Schubert polynomials for the orbits of the orthogonal group in the flag variety. These symmetric functions are also generating functions for…
Shapley value is a concept from game theory. Recently, it has been used for explaining complex models produced by machine learning techniques. Although the mathematical definition of Shapley value is straight-forward, the implication of…
It is shown that a Wishart matrix of standard complex normal random variables is asymptotically freely independent of an independent random matrix, under minimal conditions, in two different sense of asymptotic free independence.
The independence complex $\mathrm{Ind}(G)$ of a graph $G$ is the simplicial complex formed by its independent sets. This article introduces a deformation of the simplicial boundary map of $\mathrm{Ind}(G)$ that gives rise to a double…
We show that the stochastic independence of real-valued random variables is equivalent to the conditional uncorrelation, where the conditioning takes place over the Cartesian products of intervals. Next, we express the mutual independence…
We develop a topological lens on relational schema design by encoding functional dependencies (FDs) as simplices of an abstract simplicial complex. This dependency complex exposes multi-attribute interactions and enables homological…
Classical controllability and observability characterise reachability and reconstructibility of the full system state and admit equivalent geometric and eigenvalue-based Popov-Belevitch-Hautus (PBH) tests. Motivated by large-scale and…
Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding…
Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the…
In this paper, a Gaifman-Shapiro-style module architecture is tailored to the case of Smodels programs under the stable model semantics. The composition of Smodels program modules is suitably limited by module conditions which ensure the…
Uniqueness and independence are two fundamental properties of data. Their enforcement in database systems can lead to higher quality data, faster data service response time, better data-driven decision making and knowledge discovery from…
We extend upper bounds on the quantum independence number and the quantum Shannon capacity of graphs to their counterparts in the commuting operator model. We introduce a von Neumann algebraic generalization of the fractional Haemers bound…
We show that there can be no finite list of conditional independence relations which can be used to deduce all conditional independence implications among Gaussian random variables. To do this, we construct, for each $n> 3$ a family of $n$…
Traditional statistical learning theory relies on the assumption that data are identically and independently distributed (i.i.d.). However, this assumption often does not hold in many real-life applications. In this survey, we explore…
It is well-known that the notion of (strong) conditional independence (CI) is too restrictive to capture independencies that only hold in certain contexts. This kind of contextual independency, called context-strong independence (CSI), can…