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We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the…

The Broad Learning System (BLS) has gained significant attention for its computational efficiency and less network parameters compared to deep learning structures. However, the standard BLS relies on the pseudoinverse solution, which…

While Weighted Lasso sparse regression has appealing statistical guarantees that would entail a major real-world impact in finance, genomics, and brain imaging applications, it is typically scarcely adopted due to its complex…

The recursive least-squares (RLS) algorithm is one of the most well-known algorithms used in adaptive filtering, system identification and adaptive control. Its popularity is mainly due to its fast convergence speed, which is considered to…

The lasso has become an important practical tool for high dimensional regression as well as the object of intense theoretical investigation. But despite the availability of efficient algorithms, the lasso remains computationally demanding…

The latent position model (LPM) is a popular method used in network data analysis where nodes are assumed to be positioned in a $p$-dimensional latent space. The latent shrinkage position model (LSPM) is an extension of the LPM which…

The sparsity-aware zero attractor least mean square (ZA-LMS) algorithm manifests much lower misadjustment in strongly sparse environment than its sparsity-agnostic counterpart, the least mean square (LMS), but is shown to perform worse than…

We consider estimating an unknown signal, both blocky and sparse, which is corrupted by additive noise. We study three interrelated least squares procedures and their asymptotic properties. The first procedure is the fused lasso, put…

Classification and probability estimation are fundamental tasks with broad applications across modern machine learning and data science, spanning fields such as biology, medicine, engineering, and computer science. Recent development of…

In this paper, we propose two novel p-norm penalty least mean square (Lp-LMS) algorithms as supplements of the conventional Lp-LMS algorithm established for sparse adaptive filtering recently. A gradient comparator is employed to…

Despite the remarkable success of Large Language Models (LLMs), the massive size poses significant deployment challenges, particularly on resource-constrained hardware. While existing LLM compression methods focus on quantization, pruning…

Trajectory prediction plays a pivotal role in the field of intelligent vehicles. It currently suffers from several challenges,e.g., accumulative error in rollout process and weak adaptability in various scenarios. This paper proposes a…

We consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably…

Designing robust algorithms capable of training accurate neural networks on uncurated datasets from the web has been the subject of much research as it reduces the need for time consuming human labor. The focus of many previous research…

Reinforcement learning with verifiable rewards (RLVR) has recently advanced the reasoning capabilities of large language models (LLMs). While prior work has emphasized algorithmic design, data curation, and reward shaping, we investigate…

We introduce a recursive adaptive group lasso algorithm for real-time penalized least squares prediction that produces a time sequence of optimal sparse predictor coefficient vectors. At each time index the proposed algorithm computes an…

Learning from negative samples holds great promise for improving Large Language Model (LLM) reasoning capability, yet existing methods treat all incorrect responses as equally informative, overlooking the crucial role of sample quality. To…

We introduce LLM-Lasso, a novel framework that leverages large language models (LLMs) to guide feature selection in Lasso $\ell_1$ regression. Unlike traditional methods that rely solely on numerical data, LLM-Lasso incorporates…

This paper considers the estimation and prediction of a high-dimensional linear regression in the setting of transfer learning, using samples from the target model as well as auxiliary samples from different but possibly related regression…

With the increasing penetration of renewable energy, traditional physics-based power system operation faces growing challenges in achieving economic efficiency, stability, and robustness. Machine learning (ML) has emerged as a powerful tool…