相关论文: Structured Low-Rank Tensors for Generalized Linear…

Tensor-valued data arise naturally in multidimensional signal and imaging problems, such as biomedical imaging. When incorporated into generalized linear models (GLMs), naive vectorization can destroy their multi-way structure and lead to…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

We study the low-rank phase retrieval problem, where the objective is to recover a sequence of signals (typically images) given the magnitude of linear measurements of those signals. Existing solutions involve recovering a matrix…

We consider the problem of learning mixtures of generalized linear models (GLM) which arise in classification and regression problems. Typical learning approaches such as expectation maximization (EM) or variational Bayes can get stuck in…

We propose a new framework for the analysis of low-rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the…

Contingency table analysis routinely relies on log linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a low rank tensor factorization of the probability mass function for…

Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…

Growing model complexities in load modeling have created high dimensionality in parameter estimations, and thereby substantially increasing associated computational costs. In this paper, a tensor-based method is proposed for identifying…

Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper…

The Large Margin Distribution Machine (LMDM) is a recent advancement in classifier design that optimizes not just the minimum margin (as in SVM) but the entire margin distribution, thereby improving generalization. However, existing LMDM…

Recently, tensor data (or multidimensional array) have been generated in many modern applications, such as functional magnetic resonance imaging (fMRI) in neuroscience and videos in video analysis. Many efforts are made in recent years to…

In this paper we generalize and extend an idea of low-rank adaptation (LoRA) of large language models (LLMs) based on Transformer architecture. Widely used LoRA-like methods of fine-tuning LLMs are based on matrix factorization of gradient…

In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…

Statistical inference for tensors has emerged as a critical challenge in analyzing high-dimensional data in modern data science. This paper introduces a unified framework for inferring general and low-Tucker-rank linear functionals of…

Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient…

Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis. Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions. From a probabilistic perspective, these…

This article aims to seek a selection and estimation procedure for a class of tensor regression problems with multivariate covariates and matrix responses, which can provide theoretical guarantees for model selection in finite samples.…

Low-rank tensor decomposition generalizes low-rank matrix approximation and is a powerful technique for discovering low-dimensional structure in high-dimensional data. In this paper, we study Tucker decompositions and use tools from…