Related papers: Fisher Scoring for Exact Mat\'ern Covariance Estim…

In this paper, we study convex optimization methods for computing the trace norm regularized least squares estimate in multivariate linear regression. The so-called factor estimation and selection (FES) method, recently proposed by Yuan et…

We study empirical Bayes estimation in high-dimensional linear regression. To facilitate computationally efficient estimation of the underlying prior, we adopt a variational empirical Bayes approach, introduced originally in Carbonetto and…

The fuzzy linear regression (FLR) modeling was first proposed making use of linear programming and then followed by many improvements in a variety of ways. In almost all approaches changing the meters, objective function, and restrictions…

We consider Bayesian inverse problems arising in data assimilation for dynamical systems governed by partial and stochastic partial differential equations. The space-time dependent field is inferred jointly with static parameters of the…

In regression models for spatial data, it is often assumed that the marginal effects of covariates on the response are constant over space. In practice, this assumption might often be questionable. In this article, we show how a Gaussian…

In this paper, we present a novel approach to geostatistical filtering which tackles two challenges encountered when applying this method to complex spatial datasets: modeling the non-stationarity of the data while still being able to work…

The accuracy of moving horizon estimation (MHE) suffers significantly in the presence of measurement outliers. Existing methods address this issue by treating measurements leading to large MHE cost function values as outliers, which are…

Gradient-based attribution methods are model-faithful and scalable, but Integrated Gradients (IG) can be brittle because explanations depend on heuristic baselines, straight-line paths, discretization, and saturation. We propose Fisher--Rao…

This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization…

The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

Sparse regularization is a central technique for both machine learning (to achieve supervised features selection or unsupervised mixture learning) and imaging sciences (to achieve super-resolution). Existing performance guaranties assume a…

Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…

Recent advances in 3D Gaussian Splatting (3DGS) present two main directions: feed-forward models offer fast inference in sparse-view settings, while per-scene optimization yields high-quality renderings but is computationally expensive. To…

Sensor placement plays a crucial role in graph signal recovery in underdetermined systems. In this paper, we present the graph-filtered regularized maximum likelihood (GFR-ML) estimator of graph signals, which integrates general graph…

We introduce a new sequential methodology to calibrate the fixed parameters and track the stochastic dynamical variables of a state-space system. The proposed method is based on the nested hybrid filtering (NHF) framework of [1], that…

This paper presents a fast approach for penalized least squares (LS) regression problems using a 2D Gaussian Markov random field (GMRF) prior. More precisely, the computation of the proximity operator of the LS criterion regularized by…

Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem while also providing uncertainty quantification. The most popular inference algorithms for SBL exhibit prohibitively large computational costs for…

This paper considers the problem of robustly estimating the parameters of a heavy-tailed multivariate distribution when the covariance matrix is known to have the structure of a low-rank matrix plus a diagonal matrix as considered in factor…

Modeling and inferring spatial relationships and predicting missing values of environmental data are some of the main tasks of geospatial statisticians. These routine tasks are accomplished using multivariate geospatial models and the…