Related papers: A Matrix Bernstein Inequality for Strong Rayleigh …
We derive sufficient conditions for a probability measure on a finite product space (a spin system) to satisfy a (modified) logarithmic Sobolev inequality. We establish these conditions for various examples, such as the (vertex-weighted)…
We prove several trace inequalities that extend the Golden-Thompson and the Araki-Lieb-Thirring inequality to arbitrarily many matrices. In particular, we strengthen Lieb's triple matrix inequality. As an example application of our four…
Models with intractable normalizing functions have numerous applications. Because the normalizing constants are functions of the parameters of interest, standard Markov chain Monte Carlo cannot be used for Bayesian inference for these…
Neutron and X-ray reflectometry are important methods for studying thin multilayer systems. The Parratt method and the method of characteristic matrices, also referred to as transfer matrices, are used for simulation, evaluation of…
We show that the thermal subadditivity of entropy provides a common basis to derive a strong form of the bounded difference inequality and related results as well as more recent inequalities applicable to convex Lipschitz functions, random…
In information theory, the well-known log-sum inequality is a fundamental tool which indicates the non-negativity for the relative entropy. In this article, we establish a set of inequalities which are similar to the log-sum inequality…
We investigate links between the so-called Stein's density approach in dimension one and some functional and concentration inequalities. We show that measures having a finite first moment and a density with connected support satisfy a…
Linear classifiers separate the data with a hyperplane. In this paper we focus on the novel method of construction of multithreshold linear classifier, which separates the data with multiple parallel hyperplanes. Proposed model is based on…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
We prove a version of McDiarmid's bounded differences inequality for Markov chains, with constants proportional to the mixing time of the chain. We also show variance bounds and Bernstein-type inequalities for empirical averages of Markov…
Mond and Pecaric introduced a method to simplify the determination of complementary inequalities for Jensen's inequality by converting it into a single-variable maximization or minimization problem of continuous functions. This principle…
A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient…
In this article we present a Bernstein inequality for sums of random variables which are defined on a spatial lattice structure. The inequality can be used to derive concentration inequalities. It can be useful to obtain consistency…
Matrix concentration inequalities, intimately connected to the Non-Commutative Khintchine inequality, have been an important tool in both applied and pure mathematics. We study tensor versions of these inequalities, and establish…
The software Randentropy is designed to estimate inequality in a random system where several individuals interact moving among many communities and producing dependent random quantities of an attribute. The overall inequality is assessed by…
Consider an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. In order to establish concentration properties for nonlinear functions $Z(A)$, it is standard to appeal to functional inequalities like Poincar\'e or…
Reverse H\"{o}lder inequalities for a class of functions on a probability space constitute an important tool in Analysis in Probability. After revisiting how a (modified) log-Sobolev inequality can be used to derive reverse H\"{o}lder…
Langevin diffusions are rapidly convergent under appropriate functional inequality assumptions. Hence, it is natural to expect that with additional smoothness conditions to handle the discretization errors, their discretizations like the…
In this paper, we study the concentration properties of quadratic forms associated with Markov chains using the martingale decomposition method introduced by Atchad\'e and Cattaneo (2014). In particular, we derive concentration inequalities…
We present some extensions of Bernstein's concentration inequality for random matrices. This inequality has become a useful and powerful tool for many problems in statistics, signal processing and theoretical computer science. The main…