Related papers: Bayesian variational regularization on the ball

Current methods for regularization in machine learning require quite specific model assumptions (e.g. a kernel shape) that are not derived from prior knowledge about the application, but must be imposed merely to make the method work. We…

Chance constraints provide a principled framework to mitigate the risk of high-impact extreme events by modifying the controllable properties of a system. The low probability and rare occurrence of such events, however, impose severe…

We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…

Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…

We apply classical and Bayesian lasso regularizations to a family of models with the presence of mixture and process variables. We analyse the performance of these estimates with respect to ordinary least squares estimators by a simulation…

We are interested in the classical ill-posed Cauchy problem for the Laplace equation. One method to approximate the solution associated with compatible data consists in considering a family of regularized well-posed problems depending on a…

Gaussian processes are a flexible Bayesian nonparametric modelling approach that has been widely applied but poses computational challenges. To address the poor scaling of exact inference methods, approximation methods based on sparse…

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…

Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…

We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian…

We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…

We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…

We propose to use L\'evy {\alpha}-stable distributions for constructing priors for Bayesian inverse problems. The construction is based on Markov fields with stable-distributed increments. Special cases include the Cauchy and Gaussian…

In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…

Uncertainty quantification in image retrieval is crucial for downstream decisions, yet it remains a challenging and largely unexplored problem. Current methods for estimating uncertainties are poorly calibrated, computationally expensive,…

Variational Bayes (VB) has shown itself to be a powerful approximation method in many application areas. This paper describes some diagnostics methods which can assess how well the VB approximates the true posterior, particularly with…

Bayesian Neural Networks (BNNs) provide a tool to estimate the uncertainty of a neural network by considering a distribution over weights and sampling different models for each input. In this paper, we propose a method for uncertainty…

We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…

In this paper we introduce a model describing diffusion of species by a suitable regularization of a "forward-backward" parabolic equation. In particular, we prove existence and uniqueness of solutions, as well as continuous dependence on…

We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…