相关论文: Joint estimation of parameters in Ising model

In this paper, we derive distributional convergence rates for the magnetization vector and the maximum pseudolikelihood estimator of the inverse temperature parameter in the tensor Curie-Weiss Potts model. Limit theorems for the…

We study classical Ising spin-$\frac{1}{2}$ models on the 2D square lattice with ferromagnetic or antiferromagnetic nearest-neighbor interactions, under the effect of a pure imaginary magnetic field. The complex Boltzmann weights of spin…

In this paper, we consider the Ising model on random $d$-regular graphs (with $d\ge3$) and Erd\"os-R\'enyi graphs $G(n,d/n)$ (with $d>1$) at the critical temperature. We prove that the \textit{magnetization}, i.e.\ the sum of the spins of a…

This work considers parameter estimation for Gaussian process interpolation with a periodized version of the Mat{\'e}rn covariance function introduced by Stein. Convergence rates are studied for the joint maximum likelihood estimation of…

In many data analyses, each measurement may come with a simple yes/no correction; for example, belonging to one of two populations or being contaminated or not. Ignoring such binary effects may bias the results, while accounting for them…

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…

Binomial random intersection graphs can be used as parsimonious statistical models of large and sparse networks, with one parameter for the average degree and another for transitivity, the tendency of neighbours of a node to be connected.…

In [17], the authors have defined an annealed Ising model on random graphs and proved limit theorems for the magnetization of this model on some random graphs including random 2-regular graphs. Then in [11], we generalized their results to…

The rate of convergence of the Gibbs sampler for the generalized one-dimensional Ising model is determined by the second largest eigenvalue of its transition matrix in absolute value denoted by $\beta^*$. In this paper we generalize a…

We investigate a generic problem of learning pairwise exponential family graphical models with pairwise sufficient statistics defined by a global mapping function, e.g., Mercer kernels. This subclass of pairwise graphical models allow us to…

It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterisation of the phase structure, particularly in the…

The Ising model is important in statistical modeling and inference in many applications, however its normalizing constant, mean number of active vertices and mean spin interaction -- quantities needed in inference -- are computationally…

In this paper, we derive the limit of experiments for one parameter Ising models on dense regular graphs. In particular, we show that the limiting experiment is Gaussian in the low temperature regime, non Gaussian in the critical regime,…

We prove rigorously that the ferromagnetic Ising model on any nonamenable Cayley graph undergoes a continuous (second-order) phase transition in the sense that there is a unique Gibbs measure at the critical temperature. The proof of this…

We have established a quantum antiferromagnetic Heisenberg-Ising model on a spin-1/2 pyrochlore edge-shared ladder with Heisenberg intra-rung and Ising inter-rung interactions as a perspicuous candidate to exhibit magnetization mid and zero…

Given n independent Bernoulli(p) random variables X_i, i = 1, ..., n, representing the opinions of individuals connected by an underlying random k-regular graph G_n on {1, ..., n}, we show that when conditioned on an atypical empirical…

We study the pointwise maximum likelihood estimation rates for a class of Gaussian mixtures that are invariant under the action of some isometry group. This model is also known as multi-reference alignment, where random isometries of a…

Using Monte Carlo simulations we study the Ising model with spin S=1/2 and 1 on {\it directed} and {\it undirected} Erd\"os-R\'enyi (ER) random graphs, with $z$ neighbors for each spin. In the case with spin S=1/2, the {\it undirected} and…

Motivated by the home-field advantage in sports, we propose a generalized Bradley--Terry model that incorporates covariate information for paired comparisons. It has an $n$-dimensional merit parameter $\bs{\beta}$ and a fixed-dimensional…

We analyze Ising/Curie-Weiss models on the (directed) Erd\H{o}s-R\'enyi random graph on $N$ vertices in which every edge is present with probability $p$. These models were introduced by Bovier and Gayrard [J. Stat. Phys., 1993]. We prove a…