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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…
Variational inference (VI) is widely used for approximate inference in Bayesian machine learning. In addition to this practical success, generalization bounds for variational inference and related algorithms have been developed, mostly…
Variational Bayes (VB) provides a computationally efficient alternative to Markov Chain Monte Carlo, especially for high-dimensional and large-scale inference. However, existing theory on VB primarily focuses on fixed-dimensional settings…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
Distributed inference/estimation in Bayesian framework in the context of sensor networks has recently received much attention due to its broad applicability. The variational Bayesian (VB) algorithm is a technique for approximating…
Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…
Variational Bayesian posterior inference often requires simplifying approximations such as mean-field parametrisation to ensure tractability. However, prior work has associated the variational mean-field approximation for Bayesian neural…
We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…
Bayesian methods have become a popular way to incorporate prior knowledge and a notion of uncertainty into machine learning models. At the same time, the complexity of modern machine learning makes it challenging to comprehend a model's…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
Bayesian approach, as a useful tool for quantifying uncertainties, has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach for the issue is how…
Computer models play a crucial role in numerous scientific and engineering domains. To ensure the accuracy of simulations, it is essential to properly calibrate the input parameters of these models through statistical inference. While…
We introduce a novel one-parameter variational objective that lower bounds the data evidence and enables the estimation of approximate fractional posteriors. We extend this framework to hierarchical construction and Bayes posteriors,…
Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to…
Variational mean field approximations tend to struggle with contemporary overparametrized deep neural networks. Where a Bayesian treatment is usually associated with high-quality predictions and uncertainties, the practical reality has been…
Variational Bayes methods approximate the posterior density by a family of tractable distributions whose parameters are estimated by optimisation. Variational approximation is useful when exact inference is intractable or very costly. Our…
The advances in variational inference are providing promising paths in Bayesian estimation problems. These advances make variational phylogenetic inference an alternative approach to Markov Chain Monte Carlo methods for approximating the…
Weight space symmetries in neural network architectures, such as permutation symmetries in MLPs, give rise to Bayesian neural network (BNN) posteriors with many equivalent modes. This multimodality poses a challenge for variational…
Variational methods are attractive for computing Bayesian inference for highly parametrized models and large datasets where exact inference is impractical. They approximate a target distribution - either the posterior or an augmented…
Bayesian analyses combine information represented by different terms in a joint Bayesian model. When one or more of the terms is misspecified, it can be helpful to restrict the use of information from suspect model components to modify…