Related papers: Gaussian conditional independence relations have n…

Real-world complex systems are often modelled by sets of equations with endogenous and exogenous variables. What can we say about the causal and probabilistic aspects of variables that appear in these equations without explicitly solving…

The goal of this paper is to integrate the notions of stochastic conditional independence and variation conditional independence under a more general notion of extended conditional independence. We show that under appropriate assumptions…

We propose a new class of models for random permutations, which we call log-linear models, by the analogy with log-linear models used in the analysis of contingency tables. As a special case, we study the family of all Luce-decomposable…

We show that the conditional independence (CI) implication problem with bounded cardinalities, which asks whether a given CI implication holds for all discrete random variables with given cardinalities, is co-NEXPTIME-hard. The problem…

Copulas allow to learn marginal distributions separately from the multivariate dependence structure (copula) that links them together into a density function. Vine factorizations ease the learning of high-dimensional copulas by constructing…

Let $\mathbf{X}(n) \in \mathbb{R}^d$ be a sequence of random vectors, where $n\in\mathbb{N}$ and $d = d(n)$. Under certain weakly dependence conditions, we prove that the distribution of the maximal component of $\mathbf{X}$ and the…

We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…

Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to…

The fundamental concepts underlying in Markov networks are the conditional independence and the set of rules called Markov properties that translates conditional independence constraints into graphs. In this article we introduce the concept…

Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…

In this paper we present a method ofcomputing the posterior probability ofconditional independence of two or morecontinuous variables from data,examined at several resolutions. Ourapproach is motivated by theobservation that the appearance…

Let $M_n$ be the maximum of $n$ zero-mean gaussian variables $X_1,..,X_n$ with covariance matrix of minimum eigenvalue $\lambda$ and maximum eigenvalue $\Lambda$. Then, for $n \ge 70$, $$\Pr\{M_n \ge \lambda \left (2 \log n - 2.5 - \log(2…

We study a family of determinantal ideals whose decompositions encode the structural zeros in conditional independence models with hidden variables. We provide explicit decompositions of these ideals and, for certain subclasses of models,…

We prove a general independent equidistribution result for Gauss sums associated to $n$ monomials in $r$ variable multiplicative characters over a finite field, which generalizes several previous equidistribution results for Gauss and…

The paper gives a general condition on permutations, condition under which a semicircular matrix is free independent, or asymptotically free independent from the semicircular matrix obtained by permuting its entries. In particular, it is…

Inferring the causal structure that links n observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when only…

The multiresolution Gaussian process (GP) has gained increasing attention as a viable approach towards improving the quality of approximations in GPs that scale well to large-scale data. Most of the current constructions assume full…

Markov networks and Bayesian networks are effective graphic representations of the dependencies embedded in probabilistic models. It is well known that independencies captured by Markov networks (called graph-isomorphs) have a finite…

Given a Bayesian network structure (directed acyclic graph), the celebrated d-separation algorithm efficiently determines whether the network structure implies a given conditional independence relation. We show that this changes drastically…

Knowing when a graphical model is perfect to a distribution is essential in order to relate separation in the graph to conditional independence in the distribution, and this is particularly important when performing inference from data.…