Related papers: Concentration without Independence via Information…
Convergence analysis of Markov chain Monte Carlo methods in high-dimensional statistical applications is increasingly recognized. In this paper, we develop general mixing time bounds for Metropolis-Hastings algorithms on discrete spaces by…
A metric probability space $(\Omega,d)$ obeys the ${\it concentration\; of\; measure\; phenomenon}$ if subsets of measure $1/2$ enlarge to subsets of measure close to 1 as a transition parameter $\epsilon$ approaches a limit. In this paper…
Independence and conditional independence are fundamental concepts for reasoning about groups of random variables in probabilistic programs. Verification methods for independence are still nascent, and existing methods cannot handle…
The goal of this article is two-fold: in a first part, we prove Azuma-Hoeffding type concentration inequalities around the drift for the displacement of non-elementary random walks on hyperbolic spaces. For a proper hyperbolic space $M$, we…
We develop improved rearrangement algorithms to find the dependence structure that minimizes a convex function of the sum of dependent variables with given margins. We propose a new multivariate dependence measure, which can assess the…
Through a Metropolis-like algorithm with single step computational cost of order one, we build a Markov chain that relaxes to the canonical Fermi statistics for k non-interacting particles among m energy levels. Uniformly over the…
Markov chain Monte Carlo is a widely-used technique for generating a dependent sequence of samples from complex distributions. Conventionally, these methods require a source of independent random variates. Most implementations use…
Many tools exist to detect dependence between random variables, a core question across a wide range of machine learning, statistical, and scientific endeavors. Although several statistical tests guarantee eventual detection of any…
We present a new Monte Carlo algorithm that produces results of high accuracy with reduced simulational effort. Independent random walks are performed (concurrently or serially) in different, restricted ranges of energy, and the resultant…
Using concentration inequalities, we give non-asymptotic confidence intervals for estimates obtained by Markov chain Monte Carlo (MCMC) simulations, when using the approximation $\mathbb{E}_{\pi} f\approx (1/(N-t_0))\cdot \sum_{i=t_0+1}^N…
Global sensitivity analysis with variance-based measures suffers from several theoretical and practical limitations, since they focus only on the variance of the output and handle multivariate variables in a limited way. In this paper, we…
The conditional independence assumption has recently appeared in a growing body of literature on the estimation of multivariate mixtures. We consider here conditionally independent multivariate mixtures of power series distributions with…
This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…
Estimating the transition dynamics of controlled Markov chains is crucial in fields such as time series analysis, reinforcement learning, and system exploration. Traditional non-parametric density estimation methods often assume independent…
We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such…
Measuring strength or degree of statistical dependence between two random variables is a common problem in many domains. Pearson's correlation coefficient $\rho$ is an accurate measure of linear dependence. We show that $\rho$ is a…
A set of variables is the Markov blanket of a random variable if it contains all the information needed for predicting the variable. If the blanket cannot be reduced without losing useful information, it is called a Markov boundary.…
Solving partially observable Markov decision processes (POMDPs) with high dimensional and continuous observations, such as camera images, is required for many real life robotics and planning problems. Recent researches suggested machine…
A crucial assumption in most statistical learning theory is that samples are independently and identically distributed (i.i.d.). However, for many real applications, the i.i.d. assumption does not hold. We consider learning problems in…
Distance multivariance is a multivariate dependence measure, which can detect dependencies between an arbitrary number of random vectors each of which can have a distinct dimension. Here we discuss several new aspects, present a concise…