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Least squares estimation, a regression technique based on minimisation of residuals, has been invaluable in bringing the best fit solutions to parameters in science and engineering. However, in dynamic environments such as in Geomatics…
We study the problem of identifying change points in high-dimensional generalized linear models, and propose an approach based on sample-weighted empirical risk minimization. Our method, Weighted ERM, encodes priors on the change points via…
Model averaging methods have become an increasingly popular tool for improving predictions and dealing with model uncertainty, especially in Bayesian settings. Recently, frequentist model averaging methods such as information theoretic and…
A non-Bayesian, regression-based or generalized least squares (GLS)-based approach is formally proposed to estimate a class of time-varying AR parameter models. This approach has partly been used by Ito et al. (2014, 2016a,b), and is proven…
We consider the problem of robustifying high-dimensional structured estimation. Robust techniques are key in real-world applications which often involve outliers and data corruption. We focus on trimmed versions of structurally regularized…
Over the past years, there has been significant interest in understanding the implicit bias of gradient descent optimization and its connection to the generalization properties of overparametrized neural networks. Several works observed…
In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…
Penalized quantile regression (QR) is widely used for studying the relationship between a response variable and a set of predictors under data heterogeneity in high-dimensional settings. Compared to penalized least squares, scalable…
We address a specific but recurring problem related to sampled linear systems. In particular, we provide a numerical method for the rigorous verification of constraint satisfaction for linear continuous-time systems between sampling…
This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is…
Neural networks are predominantly trained using gradient-based methods, yet in many applications their final predictions remain far from the accuracy attainable within the model's expressive capacity. We introduce Linearized Subspace…
This paper addresses the problem of minimizing a convex cost function under non-negativity and equality constraints, with the aim of solving the linear unmixing problem encountered in hyperspectral imagery. This problem can be formulated as…
In this paper, we extend a previously presented Grover-based heuristic to tackle general combinatorial optimization problems with linear constraints. We further describe the introduced method as a framework that enables performance…
We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…
The generalized minimal residual (GMRES) algorithm is applied to image reconstruction using linear computed tomography (CT) models. The GMRES algorithm iteratively solves square, non-symmetric linear systems and it has practical application…
We present a new and general method of weighted least square univariate regression where the dependent variable is expanded as a series of suitably chosen functions of the independent variables. Each term of the series is obtained by an…
Two new hybrid algorithms are proposed for large-scale linear discrete ill-posed problems in general-form regularization. They are both based on Krylov subspace inner-outer iterative algorithms. At each iteration, they need to solve a…
Quantile regression (QR) can be used to describe the comprehensive relationship between a response and predictors. Prior domain knowledge and assumptions in application are usually formulated as constraints of parameters to improve the…
An interference-normalised least mean square (INLMS) algorithm for robust adaptive filtering is proposed. The INLMS algorithm extends the gradient-adaptive learning rate approach to the case where the signals are non-stationary. In…
We address the problem of sparse recovery in an online setting, where random linear measurements of a sparse signal are revealed sequentially and the objective is to recover the underlying signal. We propose a reweighted least squares (RLS)…