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We propose a fast and scalable variational method for Bayesian inference in high-dimensional parameter space, which we call projected Stein variational Newton (pSVN) method. We exploit the intrinsic low-dimensional geometric structure of…

We study data-driven decision-making problems in the Bayesian framework, where the expectation in the Bayes risk is replaced by a risk-sensitive entropic risk measure. We focus on problems where calculating the posterior distribution is…

Conformal prediction has emerged as a cutting-edge methodology in statistics and machine learning, providing prediction intervals with finite-sample frequentist coverage guarantees. Yet, its interplay with Bayesian statistics, often…

Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…

Statistical models are central to machine learning with broad applicability across a range of downstream tasks. The models are controlled by free parameters that are typically estimated from data by maximum-likelihood estimation or…

Mean Field Variational Bayes (MFVB) is a popular posterior approximation method due to its fast runtime on large-scale data sets. However, it is well known that a major failing of MFVB is its (sometimes severe) underestimates of the…

Inference models are a key component in scaling variational inference to deep latent variable models, most notably as encoder networks in variational auto-encoders (VAEs). By replacing conventional optimization-based inference with a…

Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…

Ensuring model calibration is critical for reliable prediction, yet popular distribution-free methods such as histogram binning and isotonic regression offer only asymptotic guarantees. We introduce a unified framework for Venn and…

A framework to boost the efficiency of Bayesian inference in probabilistic programs is introduced by embedding a sampler inside a variational posterior approximation. We call it the refined variational approximation. Its strength lies both…

We propose a method to approximate the distribution of robot configurations satisfying multiple objectives. Our approach uses variational inference, a popular method in Bayesian computation, which has several advantages over sampling-based…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

Topic models are Bayesian models that are frequently used to capture the latent structure of certain corpora of documents or images. Each data element in such a corpus (for instance each item in a collection of scientific articles) is…

Black-box variational inference (BBVI) now sees widespread use in machine learning and statistics as a fast yet flexible alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, stochastic optimization…

Traditional neural networks are simple to train but they typically produce overconfident predictions. In contrast, Bayesian neural networks provide good uncertainty quantification but optimizing them is time consuming due to the large…

To accelerate the inference of deep neural networks (DNNs), quantization with low-bitwidth numbers is actively researched. A prominent challenge is to quantize the DNN models into low-bitwidth numbers without significant accuracy…

Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the…

Variational Bayes (VB) is a critical method in machine learning and statistics, underpinning the recent success of Bayesian deep learning. The natural gradient is an essential component of efficient VB estimation, but it is prohibitively…

Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing…

Uncertainty quantification for full-waveform inversion provides a probabilistic characterization of the ill-conditioning of the problem, comprising the sensitivity of the solution with respect to the starting model and data noise. This…