Related papers: Conformalized Bayesian Inference, with Application…

We evaluate the robustness of a probabilistic formulation of system identification (ID) to sparse, noisy, and indirect data. Specifically, we compare estimators of future system behavior derived from the Bayesian posterior of a learning…

Estimating a distribution given access to its unnormalized density is pivotal in Bayesian inference, where the posterior is generally known only up to an unknown normalizing constant. Variational inference and Markov chain Monte Carlo…

Simulation-based inference (SBI) enables amortized Bayesian inference for simulators with implicit likelihoods. But when we are primarily interested in the quality of predictive simulations, or when the model cannot exactly reproduce the…

Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample…

We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate…

Recent advances in probabilistic deep learning enable efficient amortized Bayesian inference in settings where the likelihood function is only implicitly defined by a simulation program (simulation-based inference; SBI). But how faithful is…

We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…

Compared to mean regression and quantile regression, the literature on modal regression is very sparse. A unifying framework for Bayesian modal regression is proposed, based on a family of unimodal distributions indexed by the mode, along…

This paper introduces multimodal conformal regression. Traditionally confined to scenarios with solely numerical input features, conformal prediction is now extended to multimodal contexts through our methodology, which harnesses internal…

Conformal Prediction (CP) is a powerful statistical machine learning tool to construct uncertainty sets with coverage guarantees, which has fueled its extensive adoption in generating prediction regions for decision-making tasks, e.g.,…

Solving Bayesian inverse problems typically involves deriving a posterior distribution using Bayes' rule, followed by sampling from this posterior for analysis. Sampling methods, such as general-purpose Markov chain Monte Carlo (MCMC), are…

Some of the issues that make sampling parameter spaces of various beyond the Standard Model (BSM) scenarios computationally expensive are the high dimensionality of the input parameter space, complex likelihoods, and stringent experimental…

When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior…

We study distribution-free predictive inference for data with group symmetries, aiming to establish near-conditional coverage guarantees beyond exchangeability for structured data. While many predictive inference methods achieve a target…

Causal inference has recently gained notable attention across various fields like biology, healthcare, and environmental science, especially within explainable artificial intelligence (xAI) systems, for uncovering the causal relationships…

Loss-based clustering methods, such as k-means and its variants, are standard tools for finding groups in data. However, the lack of quantification of uncertainty in the estimated clusters is a disadvantage. Model-based clustering based on…

The Bayesian perspective on inverse problems has attracted much mathematical attention in recent years. Particular attention has been paid to Bayesian inverse problems (BIPs) in which the parameter to be inferred lies in an…

In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…

A learning-based posterior distribution estimation method, Probabilistic Dipole Inversion (PDI), is proposed to solve quantitative susceptibility mapping (QSM) inverse problem in MRI with uncertainty estimation. A deep convolutional neural…

We develop a Coordinate Ascent Variational Inference (CAVI) algorithm for Bayesian Mixed Data Sampling (MIDAS) regression with linear weight parameterizations. The model separates impact coeffcients from weighting function parameters…