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We study the problem of estimating the coefficients in linear ordinary differential equations (ODE's) with a diverging number of variables when the solutions are observed with noise. The solution trajectories are first smoothed with local…

Statistics Theory · Mathematics 2008-04-29 Heng Lian

We introduce a new method for robust beamforming, where the goal is to estimate a signal from array samples when there is uncertainty in the angle of arrival. Our method offers state-of-the-art performance on narrowband signals and is…

Signal Processing · Electrical Eng. & Systems 2024-06-25 Nakul Singh , Coleman DeLude , Mark A. Davenport , Justin Romberg

We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is…

Optimization and Control · Mathematics 2025-12-24 Zepeng Wang , Juan Peypouquet

Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…

Statistics Theory · Mathematics 2026-02-20 Florian Schäfer

This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate…

Numerical Analysis · Mathematics 2025-01-20 Elena Morotti , Davide Evangelista , Andrea Sebastiani , Elena Loli Piccolomini

Three-dimensional x-ray CT image reconstruction in baggage scanning in security applications is an important research field. The variety of materials to be reconstructed is broader than medical x-ray imaging. Presence of high attenuating…

Computer Vision and Pattern Recognition · Computer Science 2015-08-20 S. Degirmenci , Joseph A. O'Sullivan , David G. Politte

Adaptive optimizers like AdamW apply uniform hyperparameters across all parameter groups, ignoring heterogeneous optimization dynamics across layers and modules. We address this limitation by proposing MetaAdamW - a new optimizer that…

Machine Learning · Computer Science 2026-05-07 JiangBo Zhao , ZhaoXin Liu

Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…

Machine Learning · Computer Science 2026-03-31 Wan Tian , Hui Yang , Zhouhui Lian , Lingyue Zhang , Yijie Peng

In this work, we propose an observation system based on the available data which solution is one-be-one mapping to the forward problem(with the unknown initial function) solution. It implies their solutions share the same linear structure…

Numerical Analysis · Mathematics 2026-04-27 Dakang Cen , Zhiyuan Li , Wenlong Zhang

A constrained multivariate linear model is a multivariate linear model with the columns of its coefficient matrix constrained to lie in a known subspace. This class of models includes those typically used to study growth curves and…

Methodology · Statistics 2021-01-05 Dennis Cook , Liliana Forzani , Lan Liu

Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…

Computer Vision and Pattern Recognition · Computer Science 2020-10-22 Huu Le , Christopher Zach , Edward Rosten , Oliver J. Woodford

Model-based computational elasticity imaging of tissues can be posed as solving an inverse problem over finite elements spanning the displacement image. As most existing quasi-static elastography methods count on deterministic formulations…

Image and Video Processing · Electrical Eng. & Systems 2020-10-22 Narges Mohammadi , Marvin M. Doyley , Mujdat Cetin

In this paper, we focus on the numerical analysis of quantitative photoacoustic tomography. Our goal is to reconstruct the optical coefficients, i.e., the diffusion and absorption coefficients, using multiple internal observational data.…

Numerical Analysis · Mathematics 2025-05-09 Giovanni S. Alberti , Siyu Cen , Zhi Zhou

Adaptive loss function formulation is an active area of research and has gained a great deal of popularity in recent years, following the success of deep learning. However, existing frameworks of adaptive loss functions often suffer from…

Machine Learning · Computer Science 2020-01-01 A. Ali Heydari , Craig A. Thompson , Asif Mehmood

We present two versatile methods to generally enhance self-supervised monocular depth estimation (MDE) models. The high generalizability of our methods is achieved by solving the fundamental and ubiquitous problems in photometric loss…

Computer Vision and Pattern Recognition · Computer Science 2022-10-17 Xingyu Chen , Thomas H. Li , Ruonan Zhang , Ge Li

A new Levenberg--Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM method have been proposed, their main differences being in the choice of a damping…

Optimization and Control · Mathematics 2024-05-16 Naoki Marumo , Takayuki Okuno , Akiko Takeda

In many longitudinal settings, time-varying covariates may not be measured at the same time as responses and are often prone to measurement error. Naive last-observation-carried-forward methods incur estimation biases, and existing…

Methodology · Statistics 2023-03-10 Xinyue Chang , Yehua Li , Yi Li

The algorithm of modified wavelet analysis is discussed. It is based on the weighted least squares approximation. Contrary to the Gaussian as a weight function, we propose to use a compact weight function. The accuracy estimates using the…

Instrumentation and Methods for Astrophysics · Physics 2020-05-05 Ivan L. Andronov , Violetta P. Kulynska

This paper presents an algorithm for indoor layout estimation and reconstruction through the fusion of a sequence of captured images and LiDAR data sets. In the proposed system, a movable platform collects both intensity images and 2D LiDAR…

Computer Vision and Pattern Recognition · Computer Science 2020-01-16 Jieyu Li , Robert L Stevenson

We study the problem of minimizing a $m$-weakly convex and possibly nonsmooth function. Weak convexity provides a broad framework that subsumes convex, smooth, and many composite nonconvex functions. In this work, we propose a…

Optimization and Control · Mathematics 2025-09-04 Feng-Yi Liao , Yang Zheng