相关论文: Three rates of convergence or separation via U-sta…

We prove a new concentration inequality for U-statistics of order two for uniformly ergodic Markov chains. Working with bounded and $\pi$-canonical kernels, we show that we can recover the convergence rate of Arcones and Gin{\'e} who proved…

In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…

The convergence of U-statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the independence assumption is crucial [Lee90, de99]. When dealing with…

In this work, we study a natural nonparametric estimator of the transition probability matrices of a finite controlled Markov chain. We consider an offline setting with a fixed dataset, collected using a so-called logging policy. We develop…

We establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain. The constants in this inequality are explicit and depend on computable bounds on the mixing rate of the…

We study some regularity properties in locally stationary Markov models which are fundamental for controlling the bias of nonparametric kernel estimators. In particular, we provide an alternative to the standard notion of derivative process…

In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…

The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…

Markov chain Monte Carlo is widely used in a variety of scientific applications to generate approximate samples from intractable distributions. A thorough understanding of the convergence and mixing properties of these Markov chains can be…

Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…

We study the problem of clustering $T$ trajectories of length $H$, each generated by one of K unknown ergodic Markov chains over a finite state space of size $S$. We derive an instance-dependent, high-probability lower bound on the…

The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence…

We study the problem of learning the transition matrices of a set of Markov chains from a single stream of observations on each chain. We assume that the Markov chains are ergodic but otherwise unknown. The learner can sample Markov chains…

Markov chain Monte Carlo (MCMC) has transformed Bayesian model inference over the past three decades: mainly because of this, Bayesian inference is now a workhorse of applied scientists. Under general conditions, MCMC sampling converges…

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…

We propose a novel sampling-based federated learning framework for statistical inference on M-estimators with non-smooth objective functions, which frequently arise in modern statistical applications such as quantile regression and AUC…

The approximate uniform sampling of graph realizations with a given degree sequence is an everyday task in several social science, computer science, engineering etc. projects. One approach is using Markov chains. The best available current…

We use the $f-divergence$ also called relative entropy as a measure of diversity between probability densities and review its basic properties. In the sequence we define a few objects which capture relevant information from the sample of a…

We introduce Markov chain Monte Carlo (MCMC) algorithms based on numerical approximations of piecewise-deterministic Markov processes obtained with the framework of splitting schemes. We present unadjusted as well as adjusted algorithms,…

Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…