Related papers: Algebraic Study of Discrete Imsetal Models

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].…

We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many classical examples from algebraic geometry, and…

In 2010, M. Studen\'y, R. Hemmecke, and S. Linder explored a new algebraic description of graphical models, called characteristic imsets. Compare with standard imsets, characteristic imsets have several advantages: they are still unique…

We introduce a notion of non-commutative joint independence for multiple algebras in a non-commutative probability space. The pairwise relationships between these algebras are encoded by a graph with two edge sets -- a combinatorial…

Characteristic imsets are 0-1 vectors which correspond to Markov equivalence classes of directed acyclic graphs. The study of their convex hull, named the characteristic imset polytope, has led to new and interesting geometric perspectives…

Motivated by the recent work on asymptotic independence relations for random matrices with non-commutative entries, we investigate the limit distribution and independence relations for large matrices with identically distributed and Boolean…

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…

Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional…

We study a class of conditional independence models for discrete data with the property that one or more log-linear interactions are defined within two different marginal distributions and then constrained to 0; all the conditional…

This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…

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.…

Testing conditional independence has many applications, such as in Bayesian network learning and causal discovery. Different test methods have been proposed. However, existing methods generally can not work when only discretized…

The purpose of this article is to show that the bivariant algebraic $A$-cobordism groups considered previously by the author are independent of the chosen base ring $A$. This result is proven by analyzing the bivariant ideal generated by…

We define a product of algebraic probability spaces equipped with two states. This product is called a conditionally monotone product. This product is a new example of independence in non-commutative probability theory and unifies the…

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…

Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…

The paper deals with conditional linear information inequalities valid for entropy functions induced by discrete random variables. Specifically, the so-called conditional Ingleton inequalities are in the center of interest: these are valid…

The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…

The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…

Compositional graphoids are fundamental discrete structures which appear in probabilistic reasoning, particularly in the area of graphical models. They are semigraphoids which satisfy the Intersection and Composition properties. These…