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We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…

Many supervised machine learning frameworks have been proposed for disease classification using functional magnetic resonance imaging (fMRI) data, producing important biomarkers. More recently, data pooling has flourished, making the result…

The rapid scaling of large language models~(LLMs) has made inference efficiency a primary bottleneck in the practical deployment. To address this, semi-structured sparsity offers a promising solution by strategically retaining $N$ elements…

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…

The recently proposed tensor robust principal component analysis (TRPCA) methods based on tensor singular value decomposition (t-SVD) have achieved numerous successes in many fields. However, most of these methods are only applicable to…

Leading methods for support recovery in high-dimensional regression, such as Lasso, have been well-studied and their limitations in the context of correlated design have been characterized with precise incoherence conditions. In this work,…

We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…

The study of healthy brain development helps to better understand the brain transformation and brain connectivity patterns which happen during childhood to adulthood. This study presents a sparse machine learning solution across whole-brain…

Motivated by the observation that a given signal $\boldsymbol{x}$ admits sparse representations in multiple dictionaries $\boldsymbol{\Psi}_d$ but with varying levels of sparsity across dictionaries, we propose two new algorithms for the…

Large multimodal reasoning models have achieved rapid progress, but their advancement is constrained by two major limitations: the absence of open, large-scale, high-quality long chain-of-thought (CoT) data, and the instability of…

As a key component of large language model (LLM) post-training, Reinforcement Learning from Verifiable Rewards (RLVR) has substantially improved reasoning performance. However, existing RLVR algorithms exhibit distinct stability issues:…

Deep learning can help uncover patterns in resting-state functional Magnetic Resonance Imaging (rs-fMRI) associated with psychiatric disorders and personal traits. Yet the problem of interpreting deep learning findings is rarely more…

Representation based classification (RC) methods such as sparse RC (SRC) have shown great potential in face recognition in recent years. Most previous RC methods are based on the conventional regression models, such as lasso regression,…

Reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving reasoning language models on tasks such as mathematics, coding, and scientific question answering. However, widely used group-relative…

This article focuses on the robust principal component analysis (PCA) of high-dimensional data with elliptical distributions. We investigate the PCA of the sample spatial-sign covariance matrix in both nonsparse and sparse contexts,…

In this paper, we propose a regularized mixture probabilistic model to cluster matrix data and apply it to brain signals. The approach is able to capture the sparsity (low rank, small/zero values) of the original signals by introducing…

Latent factor models are the dominant backbones of contemporary recommender systems (RSs) given their performance advantages, where a unique vector embedding with a fixed dimensionality (e.g., 128) is required to represent each entity…

We propose a new sparse principal component analysis (SPCA) method in which the solutions are obtained by projecting the full cardinality principal components onto subsets of variables. The resulting components are guaranteed to explain a…