Related papers: Joint Estimation in Potts Model
Research on automated image enhancement has gained momentum in recent years, partially due to the need for easy-to-use tools for enhancing pictures captured by ubiquitous cameras on mobile devices. Many of the existing leading methods…
Consider an i.i.d. sequence of random variables whose distribution f* lies in one of a nested family of models M_q, q>=1. The smallest index q* such that M_{q*} contains f* is called the model order. We establish strong consistency of the…
The finite Gamma mixture model is often used to describe randomness in income data, insurance data, and data from other applications. The popular likelihood approach, however, does not work for this model because the likelihood function is…
The antiferromagnetic $q$-state Potts model is perhaps the most canonical model for which the uniqueness threshold on the tree is not yet understood, largely because of the absence of monotonicities. Jonasson established the uniqueness…
We derive an asymptotic expansion for the log likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for…
This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables where the functional forms are left unspecified.…
Statistical models incorporating change points are common in practice, especially in the area of biomedicine. This approach is appealing in that a specific parameter is introduced to account for the abrupt change in the response variable…
The use of reparameterization in the maximization of the likelihood function of the MA(q) model is discussed. A general method for testing for the presence of a parameter estimate on the boundary of an MA(q) model is presented. This test is…
Statistical models are widely used for the investigation of complex system's behavior. Most of the models considered in the literature are formulated on regular lattices with nearest-neighbor interactions. The models with non-local…
Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…
We propose an importance sampling scheme to estimate the partition function of the two-dimensional ferromagnetic Ising model and the two-dimensional ferromagnetic $q$-state Potts model, both in the presence of an external magnetic field.…
In this article, we propose a class of semiparametric mixture regression models with single-index. We argue that many recently proposed semiparametric/nonparametric mixture regression models can be considered special cases of the proposed…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
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Analyzing multi-layered graphical models provides insight into understanding the conditional relationships among nodes within layers after adjusting for and quantifying the effects of nodes from other layers. We obtain the penalized maximum…
Expectation Maximization (EM) is among the most popular algorithms for maximum likelihood estimation, but it is generally only guaranteed to find its stationary points of the log-likelihood objective. The goal of this article is to present…
Pairwise models like the Ising model or the generalized Potts model have found many successful applications in fields like physics, biology, and economics. Closely connected is the problem of inverse statistical mechanics, where the goal is…
Graphs from complex systems often share a partial underlying structure across domains while retaining individual features. Thus, identifying common structures can shed light on the underlying signal, for instance, when applied to scientific…
We performed Monte Carlo simulations of the two-dimensional q-state Potts model with q=10, 15, and 20 to study the energy and magnetization cumulants in the ordered and disordered phase at the first-order transition point $\beta_t$. By…
We study the Potts model on locally tree-like random graphs of arbitrary degree distribution. Using a population dynamics algorithm we numerically solve the problem exactly. We confirm our results with simulations. Comparisons with a…