Related papers: Low-rank Interaction with Sparse Additive Effects …

Constrained tensor and matrix factorization models allow to extract interpretable patterns from multiway data. Therefore identifiability properties and efficient algorithms for constrained low-rank approximations are nowadays important…

(Rephrased) Non-conformance decision-making processes in high-precision manufacturing of engineering structures are often delayed due to numerical simulations that are needed for analyzing the defective parts and assemblies. Interfaces…

We study the problem of learning mixtures of low-rank models, i.e. reconstructing multiple low-rank matrices from unlabelled linear measurements of each. This problem enriches two widely studied settings -- low-rank matrix sensing and mixed…

Within the field of hierarchical modelling, little attention is paid to micro-macro models: those in which group-level outcomes are dependent on covariates measured at the level of individuals within groups. Although such models are perhaps…

We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across…

Partial least squares (PLS) regression combines dimensionality reduction and prediction using a latent variable model. Since partial least squares regression (PLS-R) does not require matrix inversion or diagonalization, it can be applied to…

The low-rank matrix completion (LRMC) technology has achieved remarkable results in low-level visual tasks. There is an underlying assumption that the real-world matrix data is low-rank in LRMC. However, the real matrix data does not…

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…

In statistical learning framework with regressions, interactions are the contributions to the response variable from the products of the explanatory variables. In high-dimensional problems, detecting interactions is challenging due to…

We present an efficient mathematical framework based on the linearly-involved Moreau-enhanced-over-subspace (LiMES) model. Two concrete applications are considered: sparse modeling and robust regression. The popular minimax concave (MC)…

Sparse regression problems, where the goal is to identify a small set of relevant predictors, often require modeling not only main effects but also meaningful interactions through other variables. While the pliable lasso has emerged as a…

Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…

Despite the efficacy of network sparsity in alleviating the deployment strain of Large Language Models (LLMs), it endures significant performance degradation. Applying Low-Rank Adaptation (LoRA) to fine-tune the sparse LLMs offers an…

Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…

A reduced-rank mixed effects model is developed for robust modeling of sparsely observed paired functional data. In this model, the curves for each functional variable are summarized using a few functional principal components, and the…

In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…

Corrupted data sets containing noisy or missing observations are prevalent in various contemporary applications such as economics, finance and bioinformatics. Despite the recent methodological and algorithmic advances in high-dimensional…

Low-rank adaptation (LoRA) has been prominently employed for parameter-efficient fine-tuning of large language models (LLMs). However, the limited expressive capacity of LoRA, stemming from the low-rank constraint, has been recognized as a…

This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…

Registration networks have shown great application potentials in medical image analysis. However, supervised training methods have a great demand for large and high-quality labeled datasets, which is time-consuming and sometimes impractical…