Related papers: Learning the Inverse Temperature of Ising Models u…
In this paper, we have established a new framework of truncated inverse sampling for estimating mean values of non-negative random variables such as binomial, Poisson, hyper-geometrical, and bounded variables. We have derived explicit…
We consider the first-hitting time of a tempered $\beta$-stable subordinator, also called inverse tempered stable (ITS) subordinator. The density function of the ITS subordinator is obtained, for the index of stability $\beta \in (0,1)$.…
Let $A$ be a finite set and $\phi:A^Z\to R$ be a locally constant potential. For each $\beta>0$ ("inverse temperature"), there is a unique Gibbs measure $\mu_{\beta\phi}$. We prove that, as $\beta\to+\infty$, the family…
The softmax function combined with a cross-entropy loss is a principled approach to modeling probability distributions that has become ubiquitous in deep learning. The softmax function is defined by a lone hyperparameter, the temperature,…
We investigated the Ising model on a square lattice with ferro and antiferromagnetic interactions modulated by the quasiperiodic Octonacci sequence in both directions of the lattice. We have applied the Replica Exchange Monte Carlo…
We show that an high temperature expansion at fixed order parameter can be derived for the quantum Ising model. The basic point is to consider a statistical generating functional associated to the local spin state. The probability at…
An extended ensemble Monte Carlo algorithm is proposed by introducing a violation of the detailed balance condition to the update scheme of the inverse temperature in simulated tempering. Our method, irreversible simulated tempering, is…
A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading…
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…
In this article we investigate the behavior of multi-matrix unitary invariant models under a potential $V_\beta=\beta U+W$ when the inverse temperature $\beta$ becomes very large. We first prove, under mild hypothesis on the functionals…
In this paper, we study high-dimensional estimation from truncated samples. We focus on two fundamental and classical problems: (i) inference of sparse Gaussian graphical models and (ii) support recovery of sparse linear models. (i) For…
We study the performance and convergence properties of the Susceptibility Propagation (SusP) algorithm for solving the Inverse Ising problem. We first study how the temperature parameter (T) in a Sherrington-Kirkpatrick model generating the…
As in standard linear regression, in truncated linear regression, we are given access to observations $(A_i, y_i)_i$ whose dependent variable equals $y_i= A_i^{\rm T} \cdot x^* + \eta_i$, where $x^*$ is some fixed unknown vector of interest…
The Glauber dynamics of the pure and weakly disordered random-bond 2d Ising model is studied at zero-temperature. A single characteristic length scale, $L(t)$, is extracted from the equal time correlation function. In the pure case, the…
Consider the nearest-neighbor Ising model on $\Lambda_n:=[-n,n]^d\cap\mathbb{Z}^d$ at inverse temperature $\beta\geq 0$ with free boundary conditions, and let $Y_n(\sigma):=\sum_{u\in\Lambda_n}\sigma_u$ be its total magnetization. Let $X_n$…
Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…
For one-parameter continuous exponential families, we identify an unbiased estimator of the inverse of the natural parameter $\theta$ for cases where $\theta > 0$, extending an earlier result of \cite{voinov1985unbiased} applicable to a…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
This paper deals with the stochastic Ising model with a temperature shrinking to zero as time goes to infinity. A generalization of the Glauber dynamics is considered, on the basis of the existence of simultaneous flips of some spins. Such…
High-temperature series are computed for a generalized $3d$ Ising model with arbitrary potential. Two specific ``improved'' potentials (suppressing leading scaling corrections) are selected by Monte Carlo computation. Critical exponents are…