Related papers: Mean Field Variational Approximation for Continuou…

Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which…

Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as $n$ interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or…

Continuous-time Bayesian networks (CTBNs) constitute a general and powerful framework for modeling continuous-time stochastic processes on networks. This makes them particularly attractive for learning the directed structures among…

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…

Bayesian methods have shown success in deep learning applications. For example, in predictive tasks, Bayesian neural networks leverage Bayesian reasoning of model uncertainty to improve the reliability and uncertainty awareness of deep…

Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…

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…

This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…

The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmogorov equations, which is a system of linear ODEs…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational…

This article considers Bayesian model selection via mean-field (MF) variational approximation. Towards this goal, we study the non-asymptotic properties of MF inference under the Bayesian framework that allows latent variables and model…

Stochastic variational inference makes it possible to approximate posterior distributions induced by large datasets quickly using stochastic optimization. The algorithm relies on the use of fully factorized variational distributions.…

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…

Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating distribution that factorises into cluster potentials. This includes…

Mean-field models approximate large stochastic systems by simpler differential equations that are supposed to approximate the mean of the larger system. It is generally assumed that as the stochastic systems get larger (i.e., more people or…

Bayesian neural network posterior distributions have a great number of modes that correspond to the same network function. The abundance of such modes can make it difficult for approximate inference methods to do their job. Recent work has…

A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model…

This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…

Many real-world phenomena can be modelled as dynamical processes on networks, a prominent example being the spread of infectious diseases such as COVID-19. Mean-field approximations are a widely used tool to analyse such dynamical processes…