Related papers: Bayesian variational regularization on the ball
Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…
We study a regularized variant of the Bayesian Persuasion problem, where the receiver's decision process includes a divergence-based penalty that accounts for deviations from perfect rationality. This modification smooths the underlying…
In linear inverse problems, we have data derived from a noisy linear transformation of some unknown parameters, and we wish to estimate these unknowns from the data. Separable inverse problems are a powerful generalization in which the…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and…
In this paper, we consider the asymptotical regularization with convex constraints for nonlinear ill-posed problems. The method allows to use non-smooth penalty terms, including the L1-like and the total variation-like penalty functionals,…
Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…
The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation. The maximum a posteriori (MAP) estimation requires…
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…
Bayesian regression games are a special class of two-player general-sum Bayesian games in which the learner is partially informed about the adversary's objective through a Bayesian prior. This formulation captures the uncertainty in regard…
The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…
Trustworthy machine learning aims at combating distributional uncertainties in training data distributions compared to population distributions. Typical treatment frameworks include the Bayesian approach, (min-max) distributionally robust…
This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update…
Several generalizations of the traditional Tikhonov-Phillips regularization method have been proposed during the last two decades. Many of these generalizations are based upon inducing stability throughout the use of different penalizers…
In this article we show the crucial role of elliptic regularity theory for the development of efficient numerical methods for the solution of some variational problems. Here we focus to a class of elliptic multiobjective optimal control…
We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference…
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…
Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…
This paper reviews the basic ideas behind a Bayesian unfolding published some years ago and improves their implementation. In particular, uncertainties are now treated at all levels by probability density functions and their propagation is…