Related papers: Bayesian variational regularization on the ball
We introduce a new neural network-based continual learning algorithm, dubbed as Uncertainty-regularized Continual Learning (UCL), which builds on traditional Bayesian online learning framework with variational inference. We focus on two…
We refer to recent inference methodology and formulate a framework for solving the distributionally robust optimization problem, where the true probability measure is inside a Wasserstein ball around the empirical measure and the radius of…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…
In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…
The Bayesian Conjugate Gradient method (BayesCG) is a probabilistic generalization of the Conjugate Gradient method (CG) for solving linear systems with real symmetric positive definite coefficient matrices. Our CG-based implementation of…
We present a fast algorithm for the total variation regularization of the $3$-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
In the present work, we discuss variational regularization for ill-posed nonlinear problems with focus on an oversmoothing penalty term. This means in our model that the searched-for solution of the considered nonlinear operator equation…
Uncertainty quantification for image data is dominated by complex deep learning methods, yet the field lacks an interpretable, mathematically grounded baseline. We propose Bayesian scattering to fill this gap, serving as a first-step…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
We establish the first mathematically rigorous link between Bayesian, variational Bayesian, and ensemble methods. A key step towards this it to reformulate the non-convex optimisation problem typically encountered in deep learning as a…
This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows…
This paper presents an iterative scheme that converges to the solution of a pseudo-monotone variational inequality problem in the setting of $\mathbb{R}^{n}$. Traditional methods often require projections onto the feasible set…
A new method for solving stiff boundary value problems is described and compared to other known approaches using the Troesch's problem as a test example. The method is based on the general idea of alternate approximation of either the…
Regularisation allows one to handle ill-posed inverse problems. Here we focus on discrete unfolding problems. The properties of the results are characterised by the consistency between measurements and unfolding result and by the posterior…
We will consider the resolution of the 3D non linear wave equation under the assumption of spherical symmetry on the Euclidian space. For this purpose, we will build a non trivial measure on distributions such that there exists a set of…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…
Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems can be used to form an examplar measure out of various…