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We propose a new algorithm to learn the network of the interactions of pairwise Ising models. The algorithm is based on the pseudo-likelihood method (PLM), that has already been proven to efficiently solve the problem in a large variety of…
During the past decades, the Ising distribution has attracted interest in many applied disciplines, as the maximum entropy distribution associated to any set of correlated binary (`spin') variables with observed means and covariances.…
The methods of statistical physics are widely used for modelling complex networks. Building on the recently proposed Equilibrium Expectation approach, we derive a simple and efficient algorithm for maximum likelihood estimation (MLE) of…
Given a complex high-dimensional distribution over $\{\pm 1\}^n$, what is the best way to increase the expected number of $+1$'s by controlling the values of only a small number of variables? Such a problem is known as influence…
We introduce finite mixtures of Ising models as a novel approach to study multivariate patterns of associations of binary variables. Our proposed models combine the strengths of Ising models and multivariate Bernoulli mixture models. We…
Inverse Ising inference allows pairwise interactions of complex binary systems to be reconstructed from empirical correlations. Typical estimators used for this inference, such as Pseudo-likelihood maximization (PLM), are biased. Using the…
We present a probabilistic approach for the study of systems with exclusions, in the regime traditionally studied via cluster-expansion methods. In this paper we focus on its application for the gases of Peierls contours found in the study…
We propose a covariate-dependent discrete graphical model for capturing dynamic networks among discrete random variables, allowing the dependence structure among vertices to vary with covariates. This discrete dynamic network encompasses…
Gaussian mixture models are widely used to model data generated from multiple latent sources. Despite its popularity, most theoretical research assumes that the labels are either independent and identically distributed, or follows a Markov…
We assess advantages of expressing tree-structured Ising models via their mean parameterization rather than their commonly chosen canonical parameterization. This includes fixedness of marginal distributions, often convenient for dependence…
The Ising model in small-world networks generated from two- and three-dimensional regular lattices has been studied. Monte Carlo simulations were carried out to characterize the ferromagnetic transition appearing in these systems. In the…
We prove Russo-Seymour-Welsh-type uniform bounds on crossing probabilities for the FK Ising model at criticality, independent of the boundary conditions. Our proof relies mainly on Smirnov's fermionic observable for the FK Ising model,…
We consider a problem of model selection in high-dimensional binary Markov random fields. The usefulness of the Ising model in studying systems of complex interactions has been confirmed in many papers. The main drawback of this model is…
Spin glass models, such as the Sherrington-Kirkpatrick, Hopfield and Ising models, are all well-studied members of the exponential family of discrete distributions, and have been influential in a number of application domains where they are…
The Ising model is a model for pairwise interactions between binary variables that has become popular in the psychological sciences. It has been first introduced as a theoretical model for the alignment between positive (+1) and negative…
There has been a lot of work fitting Ising models to multivariate binary data in order to understand the conditional dependency relationships between the variables. However, additional covariates are frequently recorded together with the…
Influence maximization in social networks has typically been studied in the context of contagion models and irreversible processes. In this paper, we consider an alternate model that treats individual opinions as spins in an Ising system at…
Network reliability is the probability that a dynamical system composed of discrete elements interacting on a network will be found in a configuration that satisfies a particular property. We introduce a new reliability property, Ising…
We discuss a class of binary parametric families with conditional probabilities taking the form of generalized linear models and show that this approach allows to model high-dimensional random binary vectors with arbitrary mean and…
The Ising model is an equilibrium stochastic process used as a model in several branches of science including magnetic materials, geophysics, neuroscience, sociology and finance. Real systems of interest have finite size and a fixed…