Related papers: Error bounds for Approximations of Markov chains u…
In this paper, we study a notion of local stationarity for discrete time Markov chains which is useful for applications in statistics. In the spirit of some locally stationary processes introduced in the literature, we consider triangular…
This paper presents novel generalization bounds for the multi-kernel learning problem. Motivated by applications in sensor networks and spatial-temporal models, we assume that the dataset is mixed where each sample is taken from a finite…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
We consider the approximation of a convolution of possibly different probability measures by (compound) Poisson distributions and also by related signed measures of higher order. We present new total variation bounds having a better…
We present a simulation methodology for Bayesian estimation of rate parameters in Markov jump processes arising for example in stochastic kinetic models. To handle the problem of missing components and measurement errors in observed data,…
Let $\mu_N$ be the empirical measure associated to a $N$-sample of a given probability distribution $\mu$ on $\mathbb{R}^d$. We are interested in the rate of convergence of $\mu_N$ to $\mu$, when measured in the Wasserstein distance of…
We study a class of Markov chains that model the evolution of a quantum system subject to repeated measurements. Each Markov chain in this class is defined by a measure on the space of matrices. It is then given by a random product of…
We consider Bayesian analysis of a class of multiple changepoint models. While there are a variety of efficient ways to analyse these models if the parameters associated with each segment are independent, there are few general approaches…
Markov chain Monte Carlo (MCMC) methods generate samples that are asymptotically distributed from a target distribution of interest as the number of iterations goes to infinity. Various theoretical results provide upper bounds on the…
We present two data-driven procedures to estimate the transition density of an homogeneous Markov chain. The first yields to a piecewise constant estimator on a suitable random partition. By using an Hellinger-type loss, we establish…
The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining optimal risk bounds for point estimates acquired from…
Methods for Bayesian simulation in the presence of computationally intractable likelihood functions are of growing interest. Termed likelihood-free samplers, standard simulation algorithms such as Markov chain Monte Carlo have been adapted…
Bayesian methods have shown success in deep learning applications. For example, in predictive tasks, Bayesian neural networks leverage Bayesian reasoning of model uncertainty to improve the reliability and uncertainty awareness of deep…
Let $P$ be a Markov kernel on a measurable space $\X$ and let $V:\X\r[1,+\infty)$. We provide various assumptions, based on drift conditions, under which $P$ is quasi-compact on the weighted-supremum Banach space $(\cB_V,\|\cdot\|_V)$ of…
In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…
Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…
This paper develops a novel operator theoretic framework to study the contraction properties of Markov semigroups with respect to a general class of Kantorovich semi-distances, which notably includes Wasserstein distances. The rather simple…
The problem of adaptive sampling for estimating probability mass functions (pmf) uniformly well is considered. Performance of the sampling strategy is measured in terms of the worst-case mean squared error. A Bayesian variant of the…
We study fast approximation of integrals with respect to stationary probability measures associated to iterated functions systems on the unit interval. We provide an algorithm for approximating the integrals under certain conditions on 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…