Related papers: Bayesian D-Optimal Experimental Designs via Column…
Data collected from arrays of sensors are essential for informed decision-making in various systems. However, the presence of anomalies can compromise the accuracy and reliability of insights drawn from the collected data or information…
In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing…
We optimize the path of a mobile sensor to minimize the posterior uncertainty of a Bayesian inverse problem. Along its path, the sensor continuously takes measurements of the state, which is a physical quantity modeled as the solution of a…
In this work, we address the exact D-optimal experimental design problem by proposing an efficient algorithm that rapidly identifies the support of its continuous relaxation. Our method leverages a column generation framework to solve such…
Optimal experimental design (OED) concerns itself with identifying ideal methods of data collection, e.g.~via sensor placement. The \emph{greedy algorithm}, that is, placing one sensor at a time, in an iteratively optimal manner, stands as…
This paper presents a new method capable of reconstructing datasets with great precision and very low computational cost using a novel variant of the singular value decomposition (SVD) algorithm that has been named low-cost SVD (lcSVD).…
This paper provides a detailed theoretical analysis of methods to approximate the solutions of high-dimensional (>10^6) linear Bayesian problems. An optimal low-rank projection that maximizes the information content of the Bayesian…
We study statistical inverse learning in the context of nonlinear inverse problems under random design. Specifically, we address a class of nonlinear problems by employing gradient descent (GD) and stochastic gradient descent (SGD) with…
Optimal experimental design is a classic topic in statistics, with many well-studied problems, applications, and solutions. The design problem we study is the placement of sensors to monitor spatiotemporal processes, explicitly accounting…
We consider infinite-dimensional linear Gaussian Bayesian inverse problems with uncorrelated sensor data, and focus on the problem of finding sensor placements that maximize the expected information gain (EIG). This study is motivated by…
This paper investigates the sparse optimal allocation of sensors for detecting sparse leaking emission sources. Because of the non-negativity of emission rates, uncertainty associated with parameters in the forward model, and sparsity of…
In X-ray Computed Tomography (CT), projections from many angles are acquired and used for 3D reconstruction. To make CT suitable for in-line quality control, reducing the number of angles while maintaining reconstruction quality is…
In this paper, the sparse sensor placement problem for least-squares estimation is considered, and the previous novel approach of the sparse sensor selection algorithm is extended. The maximization of the determinant of the matrix which…
An energy efficient use of large scale sensor networks necessitates activating a subset of possible sensors for estimation at a fusion center. The problem is inherently combinatorial; to this end, a set of iterative, randomized algorithms…
We propose a continuous optimization algorithm for the Column Subset Selection Problem (CSSP) and Nystr\"om approximation. The CSSP and Nystr\"om method construct low-rank approximations of matrices based on a predetermined subset of…
We propose a method to optimally position a sensor system, which consists of multiple sensors, each has limited range and viewing angle, and they may fail with a certain failure rate. The goal is to find the optimal locations as well as the…
We present a mathematical framework and computational methods to optimally design a finite number of sequential experiments. We formulate this sequential optimal experimental design (sOED) problem as a finite-horizon partially observable…
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…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
In data assimilation, the model may be subject to uncertainties and errors. The weak-constraint data assimilation framework enables incorporating model uncertainty in the dynamics of the governing equations. We propose a new framework for…