Related papers: Efficient Bayesian estimation and uncertainty quan…

We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic k-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based…

Learning to infer Bayesian posterior from a few-shot dataset is an important step towards robust meta-learning due to the model uncertainty inherent in the problem. In this paper, we propose a novel Bayesian model-agnostic meta-learning…

This article tackles the old problem of prediction via a nonparametric transformation model (NTM) in a new Bayesian way. Estimation of NTMs is known challenging due to model unidentifiability though appealing because of its robust…

We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…

We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…

Manifold-valued parameters routinely arise in modern statistical applications such as in medical imaging, robotics, and computer vision, to name a few. While traditional Bayesian approaches are applicable to such settings by considering an…

Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still…

We derive posterior contraction rates (PCRs) and finite-sample Bernstein von Mises (BvM) results for non-parametric Bayesian models by extending the diffusion-based framework of Mou et al. (2024) to the infinite-dimensional setting. The…

In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…

Bayesian meta-learning enables robust and fast adaptation to new tasks with uncertainty assessment. The key idea behind Bayesian meta-learning is empirical Bayes inference of hierarchical model. In this work, we extend this framework to…

Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…

We present asymptotic results for the regression-adjusted version of approximate Bayesian computation introduced by Beaumont(2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior…

In causal inference confounding may be controlled either through regression adjustment in an outcome model, or through propensity score adjustment or inverse probability of treatment weighting, or both. The latter approaches, which are…

Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…

We consider the sparse high-dimensional linear regression model $Y=Xb+\epsilon$ where $b$ is a sparse vector. For the Bayesian approach to this problem, many authors have considered the behavior of the posterior distribution when, in truth,…

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…

Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…

The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…

Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In…