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We introduce the implicitly constrained least squares (ICLS) classifier, a novel semi-supervised version of the least squares classifier. This classifier minimizes the squared loss on the labeled data among the set of parameters implied by…

Reduced-rank regression estimates regression coefficients by imposing a low-rank constraint on the matrix of regression coefficients, thereby accounting for correlations among response variables. To further improve predictive accuracy and…

Deep learning has driven significant advances in medical image analysis, yet its adoption in clinical practice remains constrained by the large size and lack of transparency in modern models. Advances in interpretability techniques such as…

Large Language Models (LLMs) have transformed natural language processing tasks successfully. Yet, their large size and high computational needs pose challenges for practical use, especially in resource-limited settings. Model compression…

The dramatic growth of big datasets presents a new challenge to data storage and analysis. Data reduction, or subsampling, that extracts useful information from datasets is a crucial step in big data analysis. We propose an orthogonal…

Multidimensional data acquisition often requires extensive time and poses significant challenges for hardware and software regarding data storage and processing. Rather than designing a single compression matrix as in conventional…

The goal of this paper is to propose novel strategies for adaptive learning of signals defined over graphs, which are observed over a (randomly time-varying) subset of vertices. We recast two classical adaptive algorithms in the graph…

We propose a new scalable algorithm for holistic linear regression building on Bertsimas & King (2016). Specifically, we develop new theory to model significance and multicollinearity as lazy constraints rather than checking the conditions…

The impressive performance of Large Language Models (LLMs) across various natural language processing tasks comes at the cost of vast computational resources and storage requirements. One-shot pruning techniques offer a way to alleviate…

The Classification on high-dimension low-sample-size data (HDLSS) is a challenging problem and it is common to have class-imbalanced data in most application fields. We term this as Imbalanced HDLSS (IHDLSS). Recent theoretical results…

Recently, Sharma et al. suggested a method called Layer-SElective-Rank reduction (LASER) which demonstrated that pruning high-order components of carefully chosen LLM's weight matrices can boost downstream accuracy -- without any…

Efficient and scalable non-parametric or semi-parametric regression analysis and density estimation are of crucial importance to the fields of statistics and machine learning. However, available methods are limited in their ability to…

Statistical relational frameworks such as Markov logic networks and probabilistic soft logic (PSL) encode model structure with weighted first-order logical clauses. Learning these clauses from data is referred to as structure learning.…

Symbolic regression (SR) aims to discover the underlying mathematical expressions that explain observed data. This holds promise for both gaining scientific insight and for producing inherently interpretable and generalizable models for…

Predicting the mechanical properties of polysulfone (PSF) membranes from structural descriptors remains challenging due to extreme data scarcity typical of experimental studies. To investigate this issue, this study benchmarked…

In this paper, we account for approaches of sparse recovery from large underdetermined linear models with perturbation present in both the measurements and the dictionary matrix. Existing methods have high computation and low efficiency.…

To address functional-output regression, we introduce projection learning (PL), a novel dictionary-based approach that learns to predict a function that is expanded on a dictionary while minimizing an empirical risk based on a functional…

Deep learning models have achieved tremendous success in most of the industries in recent years. The evolution of these models has also led to an increase in the model size and energy requirement, making it difficult to deploy in production…

Deep neural networks (DNNs) have been quite successful in solving many complex learning problems. However, DNNs tend to have a large number of learning parameters, leading to a large memory and computation requirement. In this paper, we…

Recently, large language models (LLMs) have advanced recommendation systems (RSs), and recent works have begun to explore how to integrate LLMs into industrial RSs. While most approaches deploy LLMs offline to generate and pre-cache…