Related papers: Proper Generalized Decomposition for Nonlinear Con…

Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate…

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…

When optimization theorists consider optimization problems in infinite dimensional spaces, they need to deal with closed convex subsets(usually cones) which mostly have empty interior. These subsets often prevent optimization theorists from…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on…

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…

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…

Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. While tensors first emerged in the psychometrics community in the $20^{\text{th}}$ century, they have since then spread to…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

Tensor decomposition is a fundamental unsupervised machine learning method in data science, with applications including network analysis and sensor data processing. This work develops a generalized canonical polyadic (GCP) low-rank tensor…

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…

Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…

Large-scale neuroimaging studies have been collecting brain images of study individuals, which take the form of two-dimensional, three-dimensional, or higher dimensional arrays, also known as tensors. Addressing scientific questions arising…

In this paper we introduce the class of infinite infimal convolution functionals and apply these functionals to the regularization of ill-posed inverse problems. The proposed regularization involves an infimal convolution of a continuously…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…

We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…

Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…

Traditional tensor decomposition methods, e.g., two dimensional principal component analysis and two dimensional singular value decomposition, that minimize mean square errors, are sensitive to outliers. To overcome this problem, in this…

In recent years, there have been significant advances in the use of deep learning methods in inverse problems such as denoising, compressive sensing, inpainting, and super-resolution. While this line of works has predominantly been driven…