Related papers: Inference in Ising Models
With the growth of interest in network data across fields, the Exponential Random Graph Model (ERGM) has emerged as the leading approach to the statistical analysis of network data. ERGM parameter estimation requires the approximation of an…
This paper develops several interesting, significant, and interconnected approaches to nonparametric or semi-parametric statistical inferences. The overwhelmingly favoured maximum likelihood estimator (MLE) under parametric model is…
The ferromagnetic Ising model is a model of a magnetic material and a central topic in statistical physics. It also plays a starring role in the algorithmic study of approximate counting: approximating the partition function of the…
Spin glass models with quadratic-type Hamiltonians are disordered statistical physics systems with competing ferromagnetic and anti-ferromagnetic spin interactions. The corresponding Gibbs measures belong to the exponential family…
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,…
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…
Multiplex networks consist of a fixed set of nodes connected by several sets of edges which are generated separately and correspond to different networks ("layers"). Here, the Ising model on multiplex networks with two layers is considered,…
The ferromagnetic Ising model on an $n\times n$ square lattice region $\Lambda$ with mixed boundary conditions can exhibit a phase transition as temperature varies. For this spin system, if we fix the spins on the top and bottom sides of…
A sampling algorithm is presented that generates spin glass configurations of the 2D Edwards-Anderson Ising spin glass at finite temperature, with probabilities proportional to their Boltzmann weights. Such an algorithm overcomes the slow…
Skew normal model suffers from inferential drawbacks, namely singular Fisher information in the vicinity of symmetry and diverging of maximum likelihood estimation. To address the above drawbacks, Azzalini and Arellano-Valle (2013)…
Maximum Likelihood Estimation (MLE) is the bread and butter of system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system…
In the Ising model, we consider the problem of estimating the covariance of the spins at two specified vertices. In the ferromagnetic case, it is easy to obtain an additive approximation to this covariance by repeatedly sampling from the…
In this work we investigate partition models, the subset of log-linear models for which one can perform the iterative proportional scaling (IPS) algorithm to numerically compute the maximum likelihood estimate (MLE). Partition models…
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the…
Subsampling is a computationally effective approach to extract information from massive data sets when computing resources are limited. After a subsample is taken from the full data, most available methods use an inverse probability…
A dimer mean-field model for the Ising spin-glass is presented. Despite its simplicity it captures some of the essential features of the spin-glass physics. The distribution of the single-spin magnetization is determined from a…
Mixture of autoregressions (MoAR) models provide a model-based approach to the clustering of time series data. The maximum likelihood (ML) estimation of MoAR models requires the evaluation of products of large numbers of densities of normal…
Statistical systems on random networks can be formulated in terms of partition functions expressed with integrals by regarding Feynman diagrams as random networks. We consider the cases of random networks with bounded but generic degrees of…
We consider ferromagnetic Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the "cavity" prediction for…
The multifractal properties of the Edwards-Anderson order parameter of the short-range Ising spin glass model on d=3 diamond hierarchical lattices is studied via an exact recursion procedure. The profiles of the local order parameter are…