Related papers: Understanding Variational Inference in Function-Sp…

We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution $P_0$, which may not be in the support of the prior, we show that the posterior…

In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…

Ideally, any statistical inference should be robust to local influences. Although there are simple ways to check about leverage points in independent and linear problems, more complex models require more sophisticated methods.…

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

Performing inference in Bayesian models requires sampling algorithms to draw samples from the posterior. This becomes prohibitively expensive as the size of data sets increase. Constructing approximations to the posterior which are cheap to…

We develop a fully Bayesian framework for function-on-scalars regression with many predictors. The functional data response is modeled nonparametrically using unknown basis functions, which produces a flexible and data-adaptive functional…

The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of…

Generative models have achieved remarkable success across a range of applications, yet their evaluation still lacks principled uncertainty quantification. In this paper, we develop a method for comparing how close different generative…

Bayesian deep learning (BDL) has emerged as a principled approach to produce reliable uncertainty estimates by integrating deep neural networks with Bayesian inference, and the selection of informative prior distributions remains a…

The Kullback-Leibler (KL) divergence is frequently used in data science. For discrete distributions on large state spaces, approximations of probability vectors may result in a few small negative entries, rendering the KL divergence…

Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback-Leibler (KL) divergence, originally introduced in kinetic…

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…

This paper illustrates novel methods for nonstationary time series modeling along with their applications to selected problems in neuroscience. These methods are semi-parametric in that inferences are derived by combining sequential…

Recently, a method called the Mutual Information Neural Estimator (MINE) that uses neural networks has been proposed to estimate mutual information and more generally the Kullback-Leibler (KL) divergence between two distributions. The…

Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…

Laplace approximations are popular techniques for endowing deep networks with epistemic uncertainty estimates as they can be applied without altering the predictions of the trained network, and they scale to large models and datasets. While…

Bayesian coresets speed up posterior inference in the large-scale data regime by approximating the full-data log-likelihood function with a surrogate log-likelihood based on a small, weighted subset of the data. But while Bayesian coresets…

We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the…

Discriminator Guidance has become a popular method for efficiently refining pre-trained Score-Matching Diffusion models. However, in this paper, we demonstrate that the standard implementation of this technique does not necessarily lead to…

Bayesian inference in function space has gained attention due to its robustness against overparameterization in neural networks. However, approximating the infinite-dimensional function space introduces several challenges. In this work, we…