Related papers: On Finite Exchangeability and Conditional Independ…
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…
We introduce two new bootstraps for exchangeable random graphs. One, the "empirical graphon bootstrap", is based purely on resampling, while the other, the "histogram bootstrap", is a model-based "sieve" bootstrap. We show that both of them…
This paper investigates the robustness of strong structural controllability for linear time-invariant and linear time-varying directed networks with respect to structural perturbations, including edge deletions and additions. In this…
This paper propose a novel decomposable graphical model to accommodate skew Gaussian graphical models. We encode conditional independence structure among the components of the multivariate closed skew normal random vector by means of a…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data…
The covariance graph (aka bi-directed graph) of a probability distribution $p$ is the undirected graph $G$ where two nodes are adjacent iff their corresponding random variables are marginally dependent in $p$. In this paper, we present a…
This paper studies the problem of designing networks that are strong structurally controllable, and robust simultaneously. For given network specifications, including the number of nodes $N$, the number of leaders $N_L$, and diameter $D$,…
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.…
Using new combinatorial techniques, we significantly improve the previous results on asymptotic distributions and asymptotic free independence relations of partial transposes of Wishart random matrices. In particular, we give a necessary…
In this paper, we adopt a latent variable method to formulate a network model with arbitrarily dependent structure. We assume that the latent variables follow a multivariate normal distribution and a link between two nodes forms if the sum…
In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…
This paper present a geometric diagram of a separable state: If a mixed state $\sigma $ is separable, there are $2^{nS(\sigma)}$ linearly independant product vectors which span the same Hilbert space as the $2^{nS(\sigma)}$ ``likely''…
We show that if a strictly positive joint probability distribution for a set of binary random variables factors according to a tree, then vertex separation represents all and only the independence relations enclosed in the distribution. The…
Representing the conditional independences present in a multivariate random vector via graphs has found widespread use in applications, and such representations are popularly known as graphical models or Markov random fields. These models…
Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdos and Renyi, in particular, as well as the so-called configuration model, have served as the starting point for…
The regular models of a normal logic program are a particular type of partial (i.e. 3-valued) models which correspond to stable partial models with minimal undefinedness. In this paper, we explore graphical conditions on the dependency…
Mathematical models of stem cell differentiation are commonly based upon the concept of subsequent cell fate decisions, each controlled by a gene regulatory network. These networks exhibit a multistable behavior and cause the system to…
We consider graphs that represent pairwise marginal independencies amongst a set of variables (for instance, the zero entries of a covariance matrix for normal data). We characterize the directed acyclic graphs (DAGs) that faithfully…
A set $S$ of vertices in a graph $G = (V, E)$ is called {\em cycle independent} if the induced subgraph $\langle S\rangle$ is acyclic, and called {\em odd-cycle indepdendet} if $\langle S\rangle$ is bipartite. A set $S$ is {\em cycle…