Related papers: Sparsity-promoting hierarchical Bayesian model for…

Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing…

We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of…

In recent years, neural networks have revolutionized various domains, yet challenges such as hyperparameter tuning and overfitting remain significant hurdles. Bayesian neural networks offer a framework to address these challenges by…

Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…

Generative models based on flow matching have attracted significant attention for their simplicity and superior performance in high-resolution image synthesis. By leveraging the instantaneous change-of-variables formula, one can directly…

We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…

We propose a novel approach for sequential optimal experimental design (sOED) for Bayesian inverse problems involving expensive models with high-dimensional unknown parameters. This work focuses on designs that maximize the expected…

Inverse problems governed by partial differential equations (PDEs) play a crucial role in various fields, including computational science, image processing, and engineering. Particularly, Darcy flow equation is a fundamental equation in…

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a…

Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that reconstructs conductivity distributions within a body from boundary measurements. However, EIT reconstruction is hindered by its ill-posed nonlinear inverse…

Data collected by the Interstellar Boundary Explorer (IBEX) satellite, recording heliospheric energetic neutral atoms (ENAs), exhibit a phenomenon that has caused space scientists to revise hypotheses about the physical processes, and…

We apply a linear Bayesian model to seismic tomography, a high-dimensional inverse problem in geophysics. The objective is to estimate the three-dimensional structure of the earth's interior from data measured at its surface. Since this…

We address the problem of Bayesian reinforcement learning using efficient model-based online planning. We propose an optimism-free Bayes-adaptive algorithm to induce deeper and sparser exploration with a theoretical bound on its performance…

Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…

We evaluate the robustness of a probabilistic formulation of system identification (ID) to sparse, noisy, and indirect data. Specifically, we compare estimators of future system behavior derived from the Bayesian posterior of a learning…

In this paper, we present a practical algorithm based on sparsity regularization to effectively solve nonlinear dynamic inverse problems that are encountered in subsurface model calibration. We use an iteratively reweighted algorithm that…

Optimising black-box functions is important in many disciplines, such as tuning machine learning models, robotics, finance and mining exploration. Bayesian optimisation is a state-of-the-art technique for the global optimisation of…

Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…

An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…

This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors…