Arvind K. Saibaba
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View article: Efficient hyperparameter estimation in Bayesian inverse problems using sample average approximation
Efficient hyperparameter estimation in Bayesian inverse problems using sample average approximation Open
In Bayesian inverse problems, it is common to consider several hyperparameters that define the prior and the noise model that must be estimated from the data. In particular, we are interested in linear inverse problems with additive Gaussi…
View article: Stochastic Trace Optimization of Parameter Dependent Matrices Based on Statistical Learning Theory
Stochastic Trace Optimization of Parameter Dependent Matrices Based on Statistical Learning Theory Open
We consider matrices $\boldsymbol{A}(\boldsymbolθ)\in\mathbb{R}^{m\times m}$ that depend, possibly nonlinearly, on a parameter $\boldsymbolθ$ from a compact parameter space $Θ$. We present a Monte Carlo estimator for minimizing $\text{trac…
View article: Improved Analysis of Khatri-Rao Random Projections and Applications
Improved Analysis of Khatri-Rao Random Projections and Applications Open
Randomization has emerged as a powerful set of tools for large-scale matrix and tensor decompositions. Randomized algorithms involve computing sketches with random matrices. A prevalent approach is to take the random matrix as a standard G…
View article: Structured Column Subset Selection for Bayesian Optimal Experimental Design
Structured Column Subset Selection for Bayesian Optimal Experimental Design Open
We consider optimal experimental design (OED) for Bayesian inverse problems, where the experimental design variables have a certain multiway structure. Given $d$ different experimental variables with $m_i$ choices per design variable $1 \l…
View article: Bridging the Gap Between Deterministic and Probabilistic Approaches to State Estimation
Bridging the Gap Between Deterministic and Probabilistic Approaches to State Estimation Open
We consider the problem of state estimation from limited discrete and noisy measurements. In particular, we focus on modal state estimation, which approximates the unknown state of the system within a prescribed basis. We estimate the coef…
View article: A control-oriented approach to optimal sensor placement
A control-oriented approach to optimal sensor placement Open
We propose a control-oriented optimal experimental design (cOED) approach for linear PDE-constrained Bayesian inverse problems. In particular, we consider optimal control problems with uncertain parameters that need to be estimated by solv…
View article: Optimal sensor placement under model uncertainty in the weak-constraint 4D-Var framework
Optimal sensor placement under model uncertainty in the weak-constraint 4D-Var framework Open
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 …
View article: Parametric level-sets enhanced to improve reconstruction (PaLEnTIR)
Parametric level-sets enhanced to improve reconstruction (PaLEnTIR) Open
We introduce parametric level-set enhanced to improve reconstruction (PaLEnTIR), a significantly enhanced parametric level-set (PaLS) method addressing the restoration and reconstruction of piecewise constant objects. Our key contribution …
View article: A joint reconstruction and model selection approach for large-scale linear inverse modeling (msHyBR v2)
A joint reconstruction and model selection approach for large-scale linear inverse modeling (msHyBR v2) Open
Inverse models arise in various environmental applications, ranging from atmospheric modeling to geosciences. Inverse models can often incorporate predictor variables, similar to regression, to help estimate natural processes or parameters…
View article: Efficient hyperparameter estimation in Bayesian inverse problems using sample average approximation
Efficient hyperparameter estimation in Bayesian inverse problems using sample average approximation Open
In Bayesian inverse problems, it is common to consider several hyperparameters that define the prior and the noise model that must be estimated from the data. In particular, we are interested in linear inverse problems with additive Gaussi…
View article: Stable Rank and Intrinsic Dimension of Real and Complex Matrices
Stable Rank and Intrinsic Dimension of Real and Complex Matrices Open
The notion of `stable rank' of a matrix is central to the analysis of randomized matrix algorithms, covariance estimation, deep neural networks, and recommender systems. We compare the properties of the stable rank and intrinsic dimension …
View article: A Joint Reconstruction and Model Selection Approach for Large Scale Inverse Modeling
A Joint Reconstruction and Model Selection Approach for Large Scale Inverse Modeling Open
Inverse models arise in various environmental applications, ranging from atmospheric modeling to geosciences. Inverse models can often incorporate predictor variables, similar to regression, to help estimate natural processes or parameters…
View article: Parametric kernel low-rank approximations using tensor train decomposition
Parametric kernel low-rank approximations using tensor train decomposition Open
Computing low-rank approximations of kernel matrices is an important problem with many applications in scientific computing and data science. We propose methods to efficiently approximate and store low-rank approximations to kernel matrice…
View article: Geostatistical inverse modeling with large atmospheric data: data files for a case study from OCO-2
Geostatistical inverse modeling with large atmospheric data: data files for a case study from OCO-2 Open
The files in this data repository provide the inputs required to run an inverse modeling case study. This case study will estimate CO2 fluxes across North America for July 2015 using synthetic observations that have been created to resembl…
View article: Bayesian D-Optimal Experimental Designs via Column Subset Selection
Bayesian D-Optimal Experimental Designs via Column Subset Selection Open
This paper tackles optimal sensor placement for Bayesian linear inverse problems, a popular version of the more general Optimal Experimental Design (OED) problem, using the D-optimality criterion. This is done by establishing connections b…
View article: Randomized Preconditioned Solvers for Strong Constraint 4D-Var Data Assimilation
Randomized Preconditioned Solvers for Strong Constraint 4D-Var Data Assimilation Open
The Strong Constraint 4D Variational (SC-4DVAR) data assimilation method is widely used in climate and weather applications. SC-4DVAR involves solving a minimization problem to compute the maximum a posteriori estimate, which we tackle usi…
View article: Efficient iterative methods for hyperparameter estimation in large-scale linear inverse problems
Efficient iterative methods for hyperparameter estimation in large-scale linear inverse problems Open
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for s…
View article: Randomized low-rank approximations beyond Gaussian random matrices
Randomized low-rank approximations beyond Gaussian random matrices Open
This paper expands the analysis of randomized low-rank approximation beyond the Gaussian distribution to four classes of random matrices: (1) independent sub-Gaussian entries, (2) independent sub-Gaussian columns, (3) independent bounded c…
View article: Randomized Reduced Basis Methods for Parameterized Fractional Elliptic PDEs
Randomized Reduced Basis Methods for Parameterized Fractional Elliptic PDEs Open
This paper is interested in developing reduced order models (ROMs) for repeated simulation of fractional elliptic partial differential equations (PDEs) for multiple values of the parameters (e.g., diffusion coefficients or fractional expon…
View article: Tensor-based flow reconstruction from optimally located sensor measurements
Tensor-based flow reconstruction from optimally located sensor measurements Open
Reconstructing high-resolution flow fields from sparse measurements is a major challenge in fluid dynamics. Existing methods often vectorize the flow by stacking different spatial directions on top of each other, hence confounding the info…
View article: Randomized Algorithms for Rounding in the Tensor-Train Format
Randomized Algorithms for Rounding in the Tensor-Train Format Open
The tensor-train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential equati…
View article: A computational framework for edge-preserving regularization in dynamic inverse problems
A computational framework for edge-preserving regularization in dynamic inverse problems Open
We devise efficient methods for dynamic inverse problems, where both the quantities of interest and the forward operator (measurement process) may change in time. Our goal is to solve for all the quantities of interest simultaneously. We c…
View article: Hyper-differential sensitivity analysis in the context of Bayesian inference applied to ice-sheet problems
Hyper-differential sensitivity analysis in the context of Bayesian inference applied to ice-sheet problems Open
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model which must be estimated. Although the…
View article: Tensor-based flow reconstruction from optimally located sensor measurements
Tensor-based flow reconstruction from optimally located sensor measurements Open
Reconstructing high-resolution flow fields from sparse measurements is a major challenge in fluid dynamics. Existing methods often vectorize the flow by stacking different spatial directions on top of each other, hence confounding the info…
View article: Computationally efficient methods for large-scale atmospheric inverse modeling
Computationally efficient methods for large-scale atmospheric inverse modeling Open
Atmospheric inverse modeling describes the process of estimating greenhouse gas fluxes or air pollution emissions at the Earth's surface using observations of these gases collected in the atmosphere. The launch of new satellites, the expan…