相关论文: Doeblin Coefficients and Related Measures

We analyse diffusion dynamics on weakly-coupled networks (interconnected networks) by means of separation of time scales. Using an adiabatic approximation we reduced the system dynamics to a Markov chain with aggregated variables and…

We study the exponential dissipation of entropic functionals for continuous time Markov chains and the associated convex Sobolev inequalities, including MLSI and Beckner inequalities. We propose a method that combines the Bakry \'Emery…

In the present work, we use information theory to understand the empirical convergence rate of tractography, a widely-used approach to reconstruct anatomical fiber pathways in the living brain. Based on diffusion MRI data, tractography is…

This article studies the convergence properties of trans-dimensional MCMC algorithms when the total number of models is finite. It is shown that, for reversible and some non-reversible trans-dimensional Markov chains, under mild conditions,…

Complex networks can model the structure and dynamics of different types of systems. It has been shown that they are characterized by a set of measures. In this work, we evaluate the variability of complex networks measures face to…

The Pearson correlation coefficient is commonly used for quantifying the global level of degree-degree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the…

We propose an extension of the Contextual Graph Markov Model, a deep and probabilistic machine learning model for graphs, to model the distribution of edge features. Our approach is architectural, as we introduce an additional Bayesian…

We develop a general framework for studying ergodicity of order-preserving Markov semigroups. We establish natural and in a certain sense optimal conditions for existence and uniqueness of the invariant measure and exponential convergence…

We consider a Markov chain on $\mathbb{R}^d$ with invariant measure $\mu$. We are interested in the rate of convergence of the empirical measures towards the invariant measure with respect to various dual distances, including in particular…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

Mixing of materials is fundamental to many natural phenomena and engineering applications. The presence of discontinuous deformations - such as shear banding or wall slip - creates new mechanisms for mixing and transport beyond those…

Markov Chain Monte Carlo (MCMC) algorithms are often used for approximate inference inside learning, but their slow mixing can be difficult to diagnose and the approximations can seriously degrade learning. To alleviate these issues, we…

One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…

Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…

Using an information theoretic point of view, we investigate how a dynamics acting on a network can be coarse grained through the use of graph partitions. Specifically, we are interested in how aggregating the state space of a Markov…

The ability to compute the exact divergence between two high-dimensional distributions is useful in many applications but doing so naively is intractable. Computing the alpha-beta divergence -- a family of divergences that includes the…

An MN-Gallager Code over Galois fields, $q$, based on the Dynamical Block Posterior probabilities (DBP) for messages with a given set of autocorrelations is presented with the following main results: (a) for a binary symmetric channel the…

This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components. First, we present a general theory for strong identifiability,…

We report on a linear Langevin model that describes the evolution of the roughness of two interfaces that move towards each other and are coupled by a diffusion field. This model aims at describing the closing of the gap between two…

In this paper, a new bivariate discrete distribution is introduced which called bivariate discrete exponentiated Weibull (BDEW) distribution. Several of its mathematical statistical properties are derived such as the joint cumulative…