Related papers: Functional Tensor Regression
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…
Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. In this paper, we propose a novel nonparametric covariance function estimation…
Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…
Functional tensor decomposition can analyze multi-dimensional data with real-valued indices, paving the path for applications in machine learning and signal processing. A limitation of existing approaches is the assumption that the tensor…
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…
In this work, we describe advanced numerical tools for working with multivariate functions and for the analysis of large data sets. These tools will drastically reduce the required computing time and the storage cost, and, therefore, will…
Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…
Fitting regression models with many multivariate responses and covariates can be challenging, but such responses and covariates sometimes have tensor-variate structure. We extend the classical multivariate regression model to exploit such…
We introduce a novel longitudinal mixed model for analyzing complex multidimensional functional data, addressing challenges such as high-resolution, structural complexities, and computational demands. Our approach integrates dimension…
Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…
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…
Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and…
Dynamic multilayer networks are frequently used to describe the structure and temporal evolution of multiple relationships among common entities, with applications in fields such as sociology, economics, and neuroscience. However,…
Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative…
We propose a nested reduced-rank regression (NRRR) approach in fitting regression model with multivariate functional responses and predictors, to achieve tailored dimension reduction and facilitate interpretation/visualization of the…
We evaluate some methods designed for tensor- (or data-) based multivariate model construction (approximation and compression). To this aim, a collection of multivariate functions and an evaluation methodology are suggested. First, these…
Tensor Factor Models (TFM) are appealing dimension reduction tools for high-order large-dimensional tensor time series, and have wide applications in economics, finance and medical imaging. In this paper, we propose a projection estimator…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank…
In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…