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In the present work, we derive functional upper bounds for the potential error arising from finite-element boundary-element coupling formulations for a nonlinear Poisson-type transmission problem. The proposed a posteriori error estimates…
Model Compression has drawn much attention within the deep learning community recently. Compressing a dense neural network offers many advantages including lower computation cost, deployability to devices of limited storage and memories,…
In regression analysis of counts, a lack of simple and efficient algorithms for posterior computation has made Bayesian approaches appear unattractive and thus underdeveloped. We propose a lognormal and gamma mixed negative binomial (NB)…
This paper studies a novel approach for approximating the behavior of compartmental spreading processes. In contrast to prior work, the methods developed describe a dynamics which bound the exact moment dynamics, without explicitly…
We study how to communicate findings of Bayesian inference to third parties, while preserving the strong guarantee of differential privacy. Our main contributions are four different algorithms for private Bayesian inference on…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
Bayesian simulation-based inference (SBI) methods are used in statistical models where simulation is feasible but the likelihood is intractable. Standard SBI methods can perform poorly in cases of model misspecification, and there has been…
Under model misspecification, it is known that Bayesian posteriors often do not properly quantify uncertainty about true or pseudo-true parameters. Even more fundamentally, misspecification leads to a lack of reproducibility in the sense…
Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from…
With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in…
Prediction is a central task of statistics and machine learning, yet many inferential settings provide only partial information, typically in the form of moment constraints or estimating equations. We develop a finite, fully Bayesian…
We develop a formalism for constructing stochastic upper bounds on the expected full sample risk for supervised classification tasks via the Hilbert coresets approach within a transductive framework. We explicitly compute tight and…
Effective bounds on the union probability are well known to be beneficial in the analysis of stochastic problems in many areas, including probability theory, information theory, statistical communications, computing and operations research.…
Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an…
We present two methods for bounding the probabilities of benefit and harm under unmeasured confounding. The first method computes the (upper or lower) bound of either probability as a function of the observed data distribution and two…
The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal…
A new method is proposed for exploiting causal independencies in exact Bayesian network inference. A Bayesian network can be viewed as representing a factorization of a joint probability into the multiplication of a set of conditional…
This paper focuses on parameter estimation and introduces a new method for lower bounding the Bayesian risk. The method allows for the use of virtually \emph{any} information measure, including R\'enyi's $\alpha$, $\varphi$-Divergences, and…
This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and…
Deep neural networks are prone to overconfident predictions on outliers. Bayesian neural networks and deep ensembles have both been shown to mitigate this problem to some extent. In this work, we aim to combine the benefits of the two…