Related papers: Algebraic Aspects of Conditional Independence and …
We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary…
We introduce and study the concept which we call the splitting of a graph and compare algebraic properties of the edge ideals of graphs and those of their splitting graphs.
Recently, Forr\'e (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes…
We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such…
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…
Graphical models provide a powerful methodology for learning the conditional independence structure in multivariate data. Inference is often focused on estimating individual edges in the latent graph. Nonetheless, there is increasing…
We initiate an investigation how the fundamental concept of independence can be represented effectively in the presence of incomplete information in relational databases. The concepts of possible and certain independence are proposed, and…
In this monography, it is proposed to consider the concepts of spectra of edge cuts and edge cycles of a graph as a basic mathematical structure for solving the problem of graph isomorphism. An edge cut is defined by an edge and the…
Subobject independence as morphism co-possibility has recently been defined in [2] and studied in the context of algebraic quantum field theory. This notion of independence is handy when it comes to systems coming from physics, but when…
Testing conditional independence between two random vectors given a third is a fundamental and challenging problem in statistics, particularly in multivariate nonparametric settings due to the complexity of conditional structures. We…
We consider ideals arising in the context of conditional independence models that generalize the class of ideals considered by Fink [7] in a way distinct from the generalizations of Herzog-Hibi-Hreinsdottir-Kahle-Rauh [13] and Ay-Rauh [1].…
In this memoir, we seek to construct a constructive theory that is as complete as possible to describe the algebraic properties of the real number field in constructive mathematics without a dependent choice axiom. To this purpose, we use a…
This book is expository and is in Russian. It is shown how in the course of solution of interesting geometric problems (close to applications) naturally appear main notions of algebraic topology (homology groups, obstructions and…
Pearl and Verma developed d-separation as a widely used graphical criterion to reason about the conditional independencies that are implied by the causal structure of a Bayesian network. As acyclic ground probabilistic logic programs…
This is a short report on the discussions of appearance of tensors in algebraic statistics and rigidity theory, during the semester ``AGATES: Algebraic Geometry with Applications to TEnsors and Secants". We briefly survey some of the…
In this paper it is shown that it is possible to associate several polynomial ideals to a directed graph $D$ in order to find properties of it. In fact by using algebraic tools it is possible to give appropriate procedures for automatic…
Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed…
We develop a theory of boundary functions for ideals in trivially analytic subalgebras of simple AF C*-algebras with an injective 0-cocycle, a class which includes all full nest algebras. Boundary functions are maps from the spectrum of the…
Numerous formalisms and dedicated algorithms have been designed in the last decades to model and solve decision making problems. Some formalisms, such as constraint networks, can express "simple" decision problems, while others are designed…
We present a graphical approach to deriving inequality constraints for directed acyclic graph (DAG) models, where some variables are unobserved. In particular we show that the observed distribution of a discrete model is always restricted…