Related papers: Independence in computable algebra
We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks and conditional independence constraints on the probability distributions modeled by these networks. Our framework…
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 indicate a way of distinguishing between structures, for which, two structures are said to be separable.Being separable implies being non-isomorphic. We show that for any first order theory $T$ in a countable language, if it has an…
Inference in current domains of application are often complex and require us to integrate the expertise of a variety of disparate panels of experts and models coherently. In this paper we develop a formal statistical methodology to guide…
Let $C,A$ be countable abelian groups. In this paper we determine the complexity of classifying extensions $C$ by $A$, in the cases when $C$ is torsion-free and $A$ is a $p$-group, a torsion group with bounded primary components, or a free…
We develop a domain-theoretic framework for imprecise probability reasoning and inference on general topological spaces with a countably based continuous lattice of open sets. We address two distinct forms of uncertainty: partial or…
Independence and conditional independence are fundamental concepts for reasoning about groups of random variables in probabilistic programs. Verification methods for independence are still nascent, and existing methods cannot handle…
The non-commutative algebraic analog of the moduli of vector and covector fields is built. The structure of moduli of derivations of non-commutative algebras are studied. The canonical coupling is introduced and the conditions for…
We combine two recent ideas: cartesian differential categories, and restriction categories. The result is a new structure which axiomatizes the category of smooth maps defined on open subsets of $\R^n$ in a way that is completely algebraic.…
Expert systems applications that involve uncertain inference can be represented by a multidimensional contingency table. These tables offer a general approach to inferring with uncertain evidence, because they can embody any form of…
It is proved that, in certain subgroups of direct products of countable groups, the property of being an unconditionally closed set coincides with that of being an algebraic set. In particular, these properties coincide in all Abelian…
We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…
We embark on a tour that takes us through four closely related topics: the dual concepts of independence and spanning in finite abelian groups and the analogous dual concepts of designs and distance sets on spheres. We review some of the…
We show that a given set of first class constraints becomes abelian if one maps each constraint to the surface of other constraints. There is no assumption that first class constraints satisfy a closed algebra. The explicit form of the…
In this note, we describe how the study of backgrounds for general quantum systems can be formulated in terms of the representation theory of abstract $C^*$ algebras. We illustrate our general framework through two example systems:…
The question of which separable C*-algebras have abelian central sequence algebras was raised and studied by Phillips ([Ph88]) and Ando-Kirchberg ([AK14]). In this paper we give a complete answer to their question: A separable C*-algebra…
Abstract algebra provides a large hierarchy of properties that a collection of objects can satisfy, such as forming an abelian group or a semiring. These classifications can arranged into a broad and typically acyclic directed graph. This…
In this paper we extend the approach of M. Cavaleri to effective amenability to the class of computably enumerable groups, i.e. in particular we do not assume that groups are finitely generated. In the case of computable groups we also…
Two important notions of integrability for discrete mappings are algebraic integrability and singularity confinement, have been used for discrete mappings. Algebraic integrability is related to the existence of sufficiently many conserved…
We define an analogue of the Fox derivatives for differential polynomial algebras and give a criterion for differential algebraic dependence of a finite system of elements. In particular, we prove that differential algebraic dependence of a…