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Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…
Normalizing flows can generate complex target distributions and thus show promise in many applications in Bayesian statistics as an alternative or complement to MCMC for sampling posteriors. Since no data set from the target posterior…
Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of the final application,…
A crucial task in predictive maintenance is estimating the remaining useful life of physical systems. In the last decade, deep learning has improved considerably upon traditional model-based and statistical approaches in terms of predictive…
Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural…
Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…
In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
We propose an algorithm to estimate the path-gradient of both the reverse and forward Kullback-Leibler divergence for an arbitrary manifestly invertible normalizing flow. The resulting path-gradient estimators are straightforward to…
Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback-Leibler divergence between two sparsely sampled…
Bayesian networks (BNs) are a foundational model in machine learning and causal inference. Their graphical structure can handle high-dimensional problems, divide them into a sparse collection of smaller ones, underlies Judea Pearl's…
Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense…
Predictions made by deep learning models are prone to data perturbations, adversarial attacks, and out-of-distribution inputs. To build a trusted AI system, it is therefore critical to accurately quantify the prediction uncertainties. While…
Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an…
For linear inverse problems with a large number of unknown parameters, uncertainty quantification remains a challenging task. In this work, we use Krylov subspace methods to approximate the posterior covariance matrix and describe efficient…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…
Approximate Bayesian Computation (ABC) enables statistical inference in simulator-based models whose likelihoods are difficult to calculate but easy to simulate from. ABC constructs a kernel-type approximation to the posterior distribution…
Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Despite the growing literature about uncertainty quantification in…
Deep neural networks(NNs) have achieved impressive performance, often exceed human performance on many computer vision tasks. However, one of the most challenging issues that still remains is that NNs are overconfident in their predictions,…
Bayesian modelling allows for the quantification of predictive uncertainty which is crucial in safety-critical applications. Yet for many machine learning (ML) algorithms, it is difficult to construct or implement their Bayesian…