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We use the theory of graph limits to study several quasi-random properties, mainly dealing with various versions of hereditary subgraph counts. The main idea is to transfer the properties of (sequences of) graphs to properties of graphons,…

In a decision problem, observations are said to be material if they must be taken into account to perform optimally. Decision problems have an underlying (graphical) causal structure, which may sometimes be used to evaluate certain…

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…

Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and…

In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…

We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…

In this paper, we obtain a sufficient condition for the existence of parity factors in a regular graph in terms of edge-connectivity. Moreover, we also show that our condition is sharp.

In this work, we present a method to generate probability distributions and classes of probability distributions, which broadens a process of probability distribution construction. In this method, distribution classes are built from…

We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general exponential models. For decomposable…

Knowing when a graphical model is perfect to a distribution is essential in order to relate separation in the graph to conditional independence in the distribution, and this is particularly important when performing inference from data.…

We study graphs that are formed by independently-positioned needles (i.e., line segments) in the unit square. To mathematically characterize the graph structure, we derive the probability that two line segments intersect and determine…

The connection between contextuality and graph theory has led to many developments in the field. In particular, the sets of probability distributions in many contextuality scenarios can be described using well known convex sets from graph…

In the study of random structures we often face a trade-off between realism and tractability, the latter typically enabled by assuming some form of independence. In this work we initiate an effort to bridge this gap by developing tools that…

We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…

Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…

Representing the conditional independences present in a multivariate random vector via graphs has found widespread use in applications, and such representations are popularly known as graphical models or Markov random fields. These models…

We develop a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set…

We raise some questions about graph polynomials, highlighting concepts and phenomena that may merit consideration in the development of a general theory. Our questions are mainly of three types: When do graph polynomials have reduction…

We propose a means to relate properties of an interconnected system to its separate component systems in the presence of cascade-like phenomena. Building on a theory of interconnection reminiscent of the behavioral approach to systems…

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…