Related papers: Iterative regularization for ensemble data assimil…
Deep ensemble methods often improve predictive performance, yet they suffer from three practical limitations: redundancy among base models that inflates computational cost and degrades conditioning, unstable weighting under…
Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing (local) maximum likelihood estimate (MLE). It can be used in an extensive range of problems, including the clustering of data based on the Gaussian…
This paper proposes a novel Bayesian framework for solving Poisson inverse problems by devising a Monte Carlo sampling algorithm which accounts for the underlying non-Euclidean geometry. To address the challenges posed by the Poisson…
Bayesian inference with empirical likelihood faces a challenge as the posterior domain is a proper subset of the original parameter space due to the convex hull constraint. We propose a regularized exponentially tilted empirical likelihood…
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…
Latent Gaussian models (LGMs) are a popular class of Bayesian hierarchical models that include Gaussian processes, as well as certain spatial models and mixed-effect models. Efficient Bayesian inference of LGMs often requires marginalizing…
The electrical impedance tomography (EIT) problem of estimating the unknown conductivity distribution inside a domain from boundary current or voltage measurements requires the solution of a nonlinear inverse problem. Sparsity promoting…
Empirical Bayes provides a powerful approach to learning and adapting to latent structure in data. Theory and algorithms for empirical Bayes have a rich literature for sequence models, but are less understood in settings where latent…
In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…
We present the Sequential Ensemble Transform (SET) method, an approach for generating approximate samples from a Bayesian posterior distribution. The method explores the posterior distribution by solving a sequence of discrete optimal…
The iterated posterior linearization filter (IPLF) is an algorithm for Bayesian state estimation that performs the measurement update using iterative statistical regression. The main result behind IPLF is that the posterior approximation is…
In the context of Bayesian inversion for scientific and engineering modeling, Markov chain Monte Carlo sampling strategies are the benchmark due to their flexibility and robustness in dealing with arbitrary posterior probability density…
We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…
The iteratively reweighted least squares method (IRLS) is a popular technique used in practice for solving regression problems. Various versions of this method have been proposed, but their theoretical analyses failed to capture the good…
Hierarchical models in Bayesian inverse problems are characterized by an assumed prior probability distribution for the unknown state and measurement error precision, and hyper-priors for the prior parameters. Combining these probability…
A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…
Accurate modeling and prediction of complex physical systems often rely on data assimilation techniques to correct errors inherent in model simulations. Traditional methods like the Ensemble Kalman Filter (EnKF) and its variants as well as…
We are interested in ensemble methods to solve multi-objective optimization problems. An ensemble Kalman method is proposed to solve a formulation of the nonlinear problem using a weighted function approach. An analysis of the mean field…
To account for measurement error (ME) in explanatory variables, Bayesian approaches provide a flexible framework, as expert knowledge about unobserved covariates can be incorporated in the prior distributions. However, given the analytic…