Related papers: Comparison Theorems for Gibbs Measures
Statistical matching methods are widely used in the social and health sciences to estimate causal effects using observational data. Often the objective is to find comparable groups with similar covariate distributions in a dataset, with the…
Classical Markov Chain Monte Carlo methods have been essential for simulating statistical physical systems and have proven well applicable to other systems with many degrees of freedom. Motivated by the statistical physics origins, Chen,…
We show that for a potential with summable variations on an irreducible sofic shift in one dimension, the equilibrium measures are precisely the shift-invariant Gibbs measures. The main tool in the proof is a preservation of Gibbsianness…
We present a uniqueness result for Gibbs point processes with interactions that come from a non-negative pair potential; in particular, we provide an explicit uniqueness region in terms of activity $z$ and inverse temperature $\beta$. The…
Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…
This paper establishes a new comparison principle for the minimum eigenvalue of a sum of independent random positive-semidefinite matrices. The principle states that the minimum eigenvalue of the matrix sum is controlled by the minimum…
Similarity functions measure how comparable pairs of elements are, and play a key role in a wide variety of applications, e.g., notions of Individual Fairness abiding by the seminal paradigm of Dwork et al., as well as Clustering problems.…
Restricted Boltzmann Machines and Deep Belief Networks have been successfully used in probabilistic generative model applications such as image occlusion removal, pattern completion and motion synthesis. Generative inference in such…
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…
Mixture models are commonly used in applications with heterogeneity and overdispersion in the population, as they allow the identification of subpopulations. In the Bayesian framework, this entails the specification of suitable prior…
The Bohigas-Giannoni-Schmit (BGS) conjecture states that the Hamiltonian of a microscopic analogue of a classical chaotic system can be modeled by a random matrix from a Gaussian ensemble. Here, this conjecture is considered in the context…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…
Gibbs sampling is a Markov Chain Monte Carlo (MCMC) method often used in Bayesian learning. MCMC methods can be difficult to deploy on parallel and distributed systems due to their inherently sequential nature. We study asynchronous Gibbs…
We provide a quantification of the uniqueness of Gibbs measure for topologically mixing countable Markov shifts with locally H\"older continuous potentials. Corollaries for speed of convergence for approximation by finite subsystems are…
In this paper, we detail and complete the existing characterizations of the decimation of the Ising model on $\Z^2$ in the generalized Gibbs context. We first recall a few features of the Dobrushin program of restoration of Gibbsianness and…
The Robbins-Monro algorithm is a recursive, simulation-based stochastic procedure to approximate the zeros of a function that can be written as an expectation. It is known that under some technical assumptions, a Gaussian convergence can be…
About forty years ago it was realized by several researchers that the essential features of certain objects of Probability theory, notably Gaussian processes and limit theorems, may be better understood if they are considered in settings…
Reeb graphs are a fundamental structure for analyzing the topological and geometric properties of scalar fields. Comparing Reeb graphs is crucial for advancing research in this domain, yet existing metrics are often computationally…
We establish a one-to-one correspondence between one-sided and two-sided regular systems of conditional probabilities on the half-line that preserves the associated chains and Gibbs measures. As an application, we determine uniqueness and…