Related papers: High-dimensional Bayesian inference via the Unadju…
We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the…
This paper explores the problem of generative modeling, aiming to simulate diverse examples from an unknown distribution based on observed examples. While recent studies have focused on quantifying the statistical precision of popular…
Estimating the normalizing constant of an unnormalized probability distribution has important applications in computer science, statistical physics, machine learning, and statistics. In this work, we consider the problem of estimating the…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
Langevin dynamics are widely used in sampling high-dimensional, non-Gaussian distributions whose densities are known up to a normalizing constant. In particular, there is strong interest in unadjusted Langevin algorithms (ULA), which…
Normalized random measures with independent increments represent a large class of Bayesian nonaprametric priors and are widely used in the Bayesian nonparametric framework. In this paper, we provide the posterior consistency analysis for…
We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…
The efficiency of a Markov sampler based on the underdamped Langevin diffusion is studied for high dimensional targets with convex and smooth potentials. We consider a classical second-order integrator which requires only one gradient…
We study the behavior of the posterior distribution in high-dimensional Bayesian Gaussian linear regression models having $p\gg n$, with $p$ the number of predictors and $n$ the sample size. Our focus is on obtaining quantitative finite…
We study the problem of sampling from strongly log-concave distributions over $\mathbb{R}^d$ using the Poisson midpoint discretization (a variant of the randomized midpoint method) for overdamped/underdamped Langevin dynamics. We prove its…
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…
Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each…
The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which…
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…
Bayesian inference plays a central role in scientific and engineering applications by enabling principled reasoning under uncertainty. However, sampling from generic probability distributions remains a computationally demanding task. This…
We study the sample complexity of Bayesian recovery for solving inverse problems with general prior, forward operator and noise distributions. We consider posterior sampling according to an approximate prior $\mathcal{P}$, and establish…
A Bayesian approach is developed for the inference of an eddy-diffusivity field from Lagrangian trajectory data. The motion of Lagrangian particles is modelled by a stochastic differential equation associated with the advection-diffusion…
In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…
This work introduces a sampling method capable of solving Bayesian inverse problems in function space. It does not assume the log-concavity of the likelihood, meaning that it is compatible with nonlinear inverse problems. The method…