Related papers: Variational Bayesian Methods for Stochastically Co…

Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes the use of VB in many…

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…

Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…

Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are…

This paper is concerned with a lesser-studied problem in the context of model-based, uncertainty quantification (UQ), that of optimization/design/control under uncertainty. The solution of such problems is hindered not only by the usual…

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…

By now Bayesian methods are routinely used in practice for solving inverse problems. In inverse problems the parameter or signal of interest is observed only indirectly, as an image of a given map, and the observations are typically further…

Few Bayesian methods for analyzing high-dimensional sparse survival data provide scalable variable selection, effect estimation and uncertainty quantification. Such methods often either sacrifice uncertainty quantification by computing…

This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…

Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…

Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…

Variational Bayes (VB) is a popular estimation method for Bayesian inference. However, most existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes their use in many important situations. Tran et…

Variational Bayes (VB) has been used to facilitate the calculation of the posterior distribution in the context of Bayesian inference of the parameters of nonlinear models from data. Previously an analytical formulation of VB has been…

Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…

Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…

Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…

The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…

Modern methods for Bayesian regression beyond the Gaussian response setting are often computationally impractical or inaccurate in high dimensions. In fact, as discussed in recent literature, bypassing such a trade-off is still an open…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational…