Related papers: A Graph-Based Inference Method for Conditional Ind…
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…
First, I introduce quantum graph theory. I also discuss a known lower bound on the independence numbers and derive from it an upper bound on the chromatic numbers of quantum graphs. Then, I construct a family of quantum graphs that can be…
Scott's graph model is a lambda-algebra based on the observation that continuous endofunctions on the lattice of sets of natural numbers can be represented via their graphs. A graph is a relation mapping finite sets of input values to…
Functional graphical models have undergone extensive development during the recent years, leading to a variety models such as the functional Gaussian graphical model, the functional copula Gaussian graphical model, the functional Bayesian…
We review some independence results in a finite axiom-schematization of classical first-order logic introduced by Norman Megill. We also prove that a certain axiom scheme of this system is independent although all of its instances are…
We consider the number of independent sets in hypergraphs, which allows us to define the independence density of countable hypergraphs. Hypergraph independence densities include a broad family of densities over graphs and relational…
In this manuscript we discuss the notion of (statistical) independence embedded in its historical context. We focus in particular on its appearance and role in number theory, concomitantly exploring the intimate connection of independence…
Graph data has a unique structure that deviates from standard data assumptions, often necessitating modifications to existing methods or the development of new ones to ensure valid statistical analysis. In this paper, we explore the notion…
In order to define graph transformations by the simultaneous application of concurrent rules, we have adopted in previous work a structure of attributed graphs stable by unions. We analyze the consequences on parallel independence, a…
Monadic stability and the more general monadic dependence (or NIP) are tameness conditions for classes of logical structures, studied in the 80's in Shelah's classification program in model theory. They recently emerged in algorithmic and…
Chain graphs give a natural unifying point of view on Markov and Bayesian networks and enlarge the potential of graphical models for description of conditional independence structures. In the paper a direct graphical separation criterion…
The criterion commonly used in directed acyclic graphs (dags) for testing graphical independence is the well-known d-separation criterion. It allows us to build graphical representations of dependency models (usually probabilistic…
The theory of colorful graphs can be developed by working in Galois field modulo (p), p > 2 and a prime number. The paper proposes a program of possible conversion of graph theory into a pleasant colorful appearance. We propose to paint the…
Learning causal relations from observational data is a fundamental problem with wide-ranging applications across many fields. Constraint-based methods infer the underlying causal structure by performing conditional independence tests.…
One of the common obstacles for learning causal models from data is that high-order conditional independence (CI) relationships between random variables are difficult to estimate. Since CI tests with conditioning sets of low order can be…
We show that the stochastic independence of real-valued random variables is equivalent to the conditional uncorrelation, where the conditioning takes place over the Cartesian products of intervals. Next, we express the mutual independence…
This paper introduces the notions of independence and conditional independence in valuation-based systems (VBS). VBS is an axiomatic framework capable of representing many different uncertainty calculi. We define independence and…
In this paper we explore the design of sequent calculi operating on graphs. For this purpose, we introduce a set of logical connectives allowing us to extend the correspondence between cographs and classical propositional formulas to any…
The implication problem for conditional independence (CI) asks whether the fact that a probability distribution obeys a given finite set of CI relations implies that a further CI statement also holds in this distribution. This problem has a…
Several types of graphs with different conditional independence interpretations --- also known as Markov properties --- have been proposed and used in graphical models. In this paper we unify these Markov properties by introducing a class…