Related papers: Randomized Iterative Solver as Iterative Refinemen…
Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity…
Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…
We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect…
The randomized row method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple…
This study presents a novel mixed-precision iterative refinement algorithm, GADI-IR, within the general alternating-direction implicit (GADI) framework, designed for efficiently solving large-scale sparse linear systems. By employing…
Purpose: Parallel imaging and compressed sensing reconstructions of large MRI datasets often have a prohibitive computational cost that bottlenecks clinical deployment, especially for 3D non-Cartesian acquisitions. One common approach is to…
Sparse recovery is ubiquitous in machine learning and signal processing. Due to the NP-hard nature of sparse recovery, existing methods are known to suffer either from restrictive (or even unknown) applicability conditions, or high…
Stability analysis of Wilkinson's iterative refinement with a relaxation IR(omega) for solving linear systems is given. It extends existing results for omega=1, i.e., for Wilkinson's iterative refinement. We assume that all computations are…
The Bayesian statistical framework provides a systematic approach to enhance the regularization model by incorporating prior information about the desired solution. For the Bayesian linear inverse problems with Gaussian noise and Gaussian…
We develop a constructive approach to estimating sparse, high-dimensional linear regression models. The approach is a computational algorithm motivated from the KKT conditions for the $\ell_0$-penalized least squares solutions. It generates…
Fine-Grained Sketch-Based Image Retrieval (FG-SBIR) aims at finding a specific image from a large gallery given a query sketch. Despite the widespread applicability of FG-SBIR in many critical domains (e.g., crime activity tracking),…
Sketch-based image retrieval (SBIR) is the task of retrieving natural images (photos) that match the semantics and the spatial configuration of hand-drawn sketch queries. The universality of sketches extends the scope of possible…
We present a new Krylov subspace recycling method for solving a linear system of equations, or a sequence of slowly changing linear systems. Our approach is to reduce the computational overhead of recycling techniques while still benefiting…
The Symbolic Regression (SR) problem, where the goal is to find a regression function that does not have a pre-specified form but is any function that can be composed of a list of operators, is a hard problem in machine learning, both…
Within a statistical learning setting, we propose and study an iterative regularization algorithm for least squares defined by an incremental gradient method. In particular, we show that, if all other parameters are fixed a priori, the…
Sparse recovery and subset selection are fundamental problems in varied communities, including signal processing, statistics and machine learning. Herein, we focus on an important greedy algorithm for these problems: Backward Stepwise…
Robust subspace estimation is fundamental to many machine learning and data analysis tasks. Iteratively Reweighted Least Squares (IRLS) is an elegant and empirically effective approach to this problem, yet its theoretical properties remain…
Fine-tuning pre-trained language models such as BERT has become a common practice dominating leaderboards across various NLP tasks. Despite its recent success and wide adoption, this process is unstable when there are only a small number of…
For an overdetermined system $\mathsf{A}\mathsf{x} \approx \mathsf{b}$ with $\mathsf{A}$ and $\mathsf{b}$ given, the least-square (LS) formulation $\min_x \, \|\mathsf{A}\mathsf{x}-\mathsf{b}\|_2$ is often used to find an acceptable…
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…