Related papers: A Diffusion Process Perspective on Posterior Contr…
We prove quantitative convergence rates at which discrete Langevin-like processes converge to the invariant distribution of a related stochastic differential equation. We study the setup where the additive noise can be non-Gaussian and…
We study the posterior contraction rates of a Bayesian method with Gaussian process priors in nonparametric regression and its plug-in property for differential operators. For a general class of kernels, we establish convergence rates of…
We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…
Bayesian density deconvolution using nonparametric prior distributions is a useful alternative to the frequentist kernel based deconvolution estimators due to its potentially wide range of applicability, straightforward uncertainty…
Parameter estimation is a foundational step in statistical modeling, enabling us to extract knowledge from data and apply it effectively. Bayesian estimation of parameters incorporates prior beliefs with observed data to infer distribution…
Density Ratio Estimation has attracted attention from the machine learning community due to its ability to compare the underlying distributions of two datasets. However, in some applications, we want to compare distributions of random…
The problem of generating random samples of high-dimensional posterior distributions is considered. The main results consist of non-asymptotic computational guarantees for Langevin-type MCMC algorithms which scale polynomially in key…
This paper studies quasi Bayesian estimation and uncertainty quantification for an unknown function that is identified by a nonparametric conditional moment restriction. We derive contraction rates for a class of Gaussian process priors.…
We investigate the asymptotic behavior of posterior distributions of regression coefficients in high-dimensional linear models as the number of dimensions grows with the number of observations. We show that the posterior distribution…
We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to…
The paper presents a generalization of the local limit theorem on the convergence of inhomogeneous Markov chains to the diffusion limit for the case where the corresponding process coefficients satisfy weak regularity conditions and…
We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…
We provide convergence guarantees in Wasserstein distance for a variety of variance-reduction methods: SAGA Langevin diffusion, SVRG Langevin diffusion and control-variate underdamped Langevin diffusion. We analyze these methods under a…
Memory effects, sometimes, can not be neglected. In the framework of continuous time random walk, memory effect is modeled by the correlated waiting times. In this paper, we derive the two-point probability distribution of the stochastic…
In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in \cite{Lohmiller98} to random differential equations. We propose new definitions of…
We study nonparametric Bayesian models for reversible multi-dimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift…
In this article we consider Bayesian estimation of static parameters for a class of partially observed McKean-Vlasov diffusion processes with discrete-time observations over a fixed time interval. This problem features several obstacles to…
Theories with a sign problem due to a complex action or Boltzmann weight can sometimes be numerically solved using a stochastic process in the complexified configuration space. However, the probability distribution effectively sampled by…
We study the rates of convergence of the posterior distribution for Bayesian density estimation with Dirichlet mixtures of normal distributions as the prior. The true density is assumed to be twice continuously differentiable. The bandwidth…
In a smooth semiparametric model, the marginal posterior distribution of the finite dimensional parameter of interest is expected to be asymptotically equivalent to the sampling distribution of frequentist's efficient estimators. This is…