Related papers: Polyhedral Aspects of Maxoids
We propose a method for inferring the conditional indepen- dence graph (CIG) of a high-dimensional discrete-time Gaus- sian vector random process from finite-length observations. Our approach does not rely on a parametric model (such as,…
Network models, which abstractly are given by lax symmetric monoidal functors, are used to construct operads for modeling and designing complex networks. Many common types of networks can be modeled with simple graphs with edges weighted by…
Conditional Independence (CI) graph is a special type of a Probabilistic Graphical Model (PGM) where the feature connections are modeled using an undirected graph and the edge weights show the partial correlation strength between the…
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…
This paper presents a framework based on matrices of monoids for the study of coupled cell networks. We formally prove within the proposed framework, that the set of results about invariant synchrony patterns for unweighted networks also…
Bayesian methods for graphical log-linear marginal models have not been developed in the same extent as traditional frequentist approaches. In this work, we introduce a novel Bayesian approach for quantitative learning for such models.…
Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and…
The use of directed acyclic graphs (DAGs) to represent conditional independence relations among random variables has proved fruitful in a variety of ways. Recursive structural equation models are one kind of DAG model. However,…
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…
The semigraphoid closure of every couple of CI-statements (GI=conditional independence) is a stochastic CI-model. As a consequence of this result it is shown that every probabilistically sound inference rule for CI-model, having at most two…
In broad applications, it is routinely of interest to assess whether there is evidence in the data to refute the assumption of conditional independence of $Y$ and $X$ conditionally on $Z$. Such tests are well developed in parametric models…
We introduce an algebraic concept of the frame for abstract conditional independence (CI) models, together with basic operations with respect to which such a frame should be closed: copying and marginalization. Three standard examples of…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
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…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
We study the problem of learning multivariate dependencies in nonparametric and high-dimensional settings. This includes but is not limited to graphical models. Our approach effectively combines several features that are missing from…
The method of imsets, introduced by Studen\'y, provides a geometric and combinatorial description of conditional independence statements. Elementary conditional independence statements over a finite set of discrete random variables…
We consider the problem of inferring the conditional independence graph (CIG) of a multivariate stationary dicrete-time Gaussian random process based on a finite length observation. Using information-theoretic methods, we derive a lower…
We study the problem of independence and conditional independence tests between categorical covariates and a continuous response variable, which has an immediate application in genetics. Instead of estimating the conditional distribution of…
We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…