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We consider a two-dimensional Ising model with random i.i.d. nearest-neighbor ferromagnetic couplings and no external magnetic field. We show that, if the probability of supercritical couplings is small enough, the system admits a…
We introduce varying spin strengths to the Ising model, a central pillar of statistical physics. With inhomogeneous physical systems in mind, but also anticipating interdisciplinary applications, we present the model on network structures…
Given samples from an unknown multivariate distribution $p$, is it possible to distinguish whether $p$ is the product of its marginals versus $p$ being far from every product distribution? Similarly, is it possible to distinguish whether…
Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes.…
Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for…
Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models,…
The Ising model on a $restricted$ scale-free network (SFN) has been studied employing Monte Carlo simulations. This network is described by a power-law degree distribution in the form $P(k)~k^{-\alpha}$, and is called restricted, because…
Inferring a generative model from data is a fundamental problem in machine learning. It is well-known that the Ising model is the maximum entropy model for binary variables which reproduces the sample mean and pairwise correlations.…
The Poisson log-normal model is a latent variable model that provides a generic framework for the analysis of multivariate count data. Inferring its parameters can be a daunting task since the conditional distribution of the latent…
Success in modeling complex phenomena such as human perception hinges critically on the availability of data and computational power. Significant progress has been made in modeling such phenomena using probabilistic methods, particularly in…
The Ising model is a simple statistical model for ferromagnetism. There are analytic solutions for low dimensions and very efficient Monte Carlo methods, such as cluster algorithms, for simulating this model in special cases. However most…
Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function and its derivatives. Here we propose a new parameter estimation technique that does not require computing an intractable…
Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models,…
Learning Gibbs distributions using only sufficient statistics has long been recognized as a computationally hard problem. On the other hand, computationally efficient algorithms for learning Gibbs distributions rely on access to full sample…
Maximum pseudolikelihood method has been among the most important methods for learning parameters of statistical physics models, such as Ising models. In this paper, we study how pseudolikelihood can be derived for learning parameters of a…
We study the problem of learning the structure and parameters of the Ising model, a fundamental model of high-dimensional data, when observing the evolution of an associated Markov chain. A recent line of work has studied the natural…
We study pairwise Ising models for describing the statistics of multi-neuron spike trains, using data from a simulated cortical network. We explore efficient ways of finding the optimal couplings in these models and examine their…
Bogdan et al. established a new criterion to determine the existence of a maximum likelihood estimator in discrete exponential families. It uses the notion of the set of uniqueness, which allows to apply the problem to the Ising model from…
We study the problem of testing, using only a single sample, between mean field distributions (like Curie-Weiss, Erd\H{o}s-R\'enyi) and structured Gibbs distributions (like Ising model on sparse graphs and Exponential Random Graphs). Our…
A wide array of complex biological, social, and physical systems have recently been shown to be quantitatively described by Ising models, which lie at the intersection of statistical physics and machine learning. Here, we study the…