Related papers: Matrix representations and independencies in direc…
We address some computational issues that may hinder the use of AMP chain graphs in practice. Specifically, we show how a discrete probability distribution that satisfies all the independencies represented by an AMP chain graph factorizes…
Given experimental data, one of the main objectives of biological modeling is to construct a model which best represents the real world phenomena. In some cases, there could be multiple distinct models exhibiting the exact same dynamics,…
We study the data-driven selection of causal graphical models using constraint-based algorithms, which determine the existence or non-existence of edges (causal connections) in a graph based on testing a series of conditional independence…
An explicit algorithm is presented for testing whether two non-directed graphs are isomorphic or not. It is shown that for a graph of n vertices, the number of n independent operations needed for the test is polynomial in n. A proof that…
We introduce the concept of pattern graphs--directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a…
Two cycles are referred as disjoint if they have no common edges. In this paper, we will investigate the determinant of the distance matrix of a graph, giving a formula for the determinant of the distance matrix of a bicyclic graph whose…
We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such…
This paper proposes a simple procedure to decide whether the empirically-observed adjacency or weights matrix, which characterizes the graph underlying a socio-economic network, is sufficiently symmetric (respectively, asymmetric) to…
The present paper introduces a modified version of cyclic-monotone independence which originally arose in the context of random matrices, and also introduces its natural analogy called cyclic-Boolean independence. We investigate formulas…
Missing data is a pervasive problem in data analyses, resulting in datasets that contain censored realizations of a target distribution. Many approaches to inference on the target distribution using censored observed data, rely on missing…
Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…
The cycles are the only $2$-connected graphs in which any two nonadjacent vertices form a vertex cut. We generalize this fact by proving that for every integer $k\ge 3$ there exists a unique graph $G$ satisfying the following conditions:…
We construct infinite families of graphs that are determined by their generalized spectrum. This construction is based on new formulae for the determinant of the walk matrix of a graph. The graphs constructed here all satisfy a lower…
For causal discovery in the presence of latent confounders, constraints beyond conditional independences exist that can enable causal discovery algorithms to distinguish more pairs of graphs. Such constraints are not well-understood yet. In…
We consider complete graphs with edge weights and/or node weights taking values in some set. In the first part of this paper, we show that a large number of graphs are completely determined, up to isomorphism, by the distribution of their…
The distance matrix of a connected graph is defined as the matrix in which the entries are the pairwise distances between vertices. The distance spectrum of a graph is the set of eigenvalues of its distance matrix. A graph is said to be…
In this paper, we study classes of graphs with three types of edges that capture the modified independence structure of a directed acyclic graph (DAG) after marginalisation over unobserved variables and conditioning on selection variables…
We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bi-directed graph models, under the global Markov property. Such models are useful data analytic tools especially…
The necessary and sufficient conditions for a function to be totally or partially separable are derived. It is shown that a function is totally separable if and only if each component of the gradient vector of depends only on the…
We study the zero sets of the independence polynomial on recursive sequences of graphs. We prove that for a maximally independent starting graph and a stable and expanding recursion algorithm, the zeros of the independence polynomial are…