相关论文: Joint estimation of parameters in Ising model

We prove a hardness of sampling result for the anti-ferromagnetic Ising model on random graphs of average degree $d$ for large constant $d$, proving that when the normalized inverse temperature satisfies $\beta>1$ (asymptotically…

In this paper, we study estimation of parameters in a two-parameter Potts model with $q$ colors and coupling matrix $A_N$. We characterize concrete sufficient conditions for existence of the pseudo-likelihood estimator of the Potts model,…

We consider the problem of estimating inverse temperature parameter $\beta$ of an $n$-dimensional truncated Ising model using a single sample. Given a graph $G = (V,E)$ with $n$ vertices, a truncated Ising model is a probability…

The Ising spin glass is a one-parameter exponential family model for binary data with quadratic sufficient statistic. In this paper, we show that given a single realization from this model, the maximum pseudolikelihood estimate (MPLE) of…

We consider the Ising model with inverse temperature beta and without external field on sequences of graphs G_n which converge locally to the k-regular tree. We show that for such graphs the Ising measure locally weak converges to the…

The main goal of the paper is to prove central limit theorems for the magnetization rescaled by $\sqrt{N}$ for the Ising model on random graphs with $N$ vertices. Both random quenched and averaged quenched measures are considered. We work…

We study the metastability of the ferromagnetic Ising model on a random $r$-regular graph in the zero temperature limit. We prove that in the presence of a small positive external field the time that it takes to go from the all minus state…

The aim of this paper is to prove central limit theorems with respect to the annealed measure for the magnetization rescaled by $\sqrt{N}$ of Ising models on random graphs. More precisely, we consider the general rank-1 inhomogeneous random…

We study the fixed-magnetization ferromagnetic Ising model on random $d$-regular graphs for $d\ge 3$ and inverse temperature below the tree reconstruction threshold. Our main result is that for each magnetization $\eta$, the free energy…

Although the fully connected Ising model does not have a length scale, we show that its critical exponents can be found using finite size scaling with the scaling variable equal to N, the number of spins. We find that at the critical…

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…

We investigate the learning performance of the pseudolikelihood maximization method for inverse Ising problems. In the teacher-student scenario under the assumption that the teacher's couplings are sparse and the student does not know the…

We provide a simple characterization of the critical temperature for the Ising model on an arbitrary planar doubly periodic weighted graph. More precisely, the critical inverse temperature \beta for a graph G with coupling constants…

When the number of subjects, $n$, is large, paired comparisons are often sparse. Here, we study statistical inference in a class of paired comparison models parameterized by a set of merit parameters, under an Erd\"{o}s--R\'{e}nyi…

Probabilistic graphical models provide a flexible yet parsimonious framework for modeling dependencies among nodes in networks. There is a vast literature on parameter estimation and consistent model selection for graphical models. However,…

The logistic regression model is one of the most popular data generation model in noisy binary classification problems. In this work, we study the sample complexity of estimating the parameters of the logistic regression model up to a given…

We consider testing for the parameters of Ferromagnetic Ising models. While testing for the presence of possibly sparse magnetizations, we provide a general lower bound of minimax separation rates which yields sharp results in high…

We consider the problem of estimating Ising models over $n$ variables in Total Variation (TV) distance, given $l$ independent samples from the model. While the statistical complexity of the problem is well-understood [DMR20], identifying…

We study the maximum and minimum occupancy fraction of the antiferromagnetic Ising model in regular graphs. The minimizing problem is known to determine a computational threshold in the complexity of approximately sampling from the Ising…

Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant…