Related papers: Tensor Canonical Correlation Analysis with Converg…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

Tensor networks such as matrix product states (MPS) and projected entangled pair states (PEPS) are commonly used to approximate quantum systems. These networks are optimized in methods such as DMRG or evolved by local operators. We provide…

Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…

Canonical Correlation Analysis (CCA) is a method for feature extraction of two views by finding maximally correlated linear projections of them. Several variants of CCA have been introduced in the literature, in particular, variants based…

We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…

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…

While post-training model compression can greatly reduce the inference cost of a deep neural network, uncompressed training still consumes a huge amount of hardware resources, run-time and energy. It is highly desirable to directly train a…

In this paper we review basic and emerging models and associated algorithms for large-scale tensor networks, especially Tensor Train (TT) decompositions using novel mathematical and graphical representations. We discus the concept of…

Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…

High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…

Learning representations of two views of data such that the resulting representations are highly linearly correlated is appealing in machine learning. In this paper, we present a canonical correlation guided learning framework, which allows…

This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…

We propose a novel data harmonization approach known as Tensor-ComBat (TC) for structural neuroimaging data. Tensor-Combat is a novel spatially aware harmonization method that aims to estimate and remove unwanted technical variation between…

This work considers low-rank canonical polyadic decomposition (CPD) under a class of non-Euclidean loss functions that frequently arise in statistical machine learning and signal processing. These loss functions are often used for certain…

We present a new accelerated stochastic second-order method that is robust to both gradient and Hessian inexactness, which occurs typically in machine learning. We establish theoretical lower bounds and prove that our algorithm achieves…

Recovering a low-rank tensor from incomplete information is a recurring problem in signal processing and machine learning. The most popular convex relaxation of this problem minimizes the sum of the nuclear norms of the unfoldings of the…

We provide a comprehensive study of the convergence of the forward-backward algorithm under suitable geometric conditions, such as conditioning or {\L}ojasiewicz properties. These geometrical notions are usually local by nature, and may…

We introduce tensor numerical techniques for solving optimal control problems constrained by elliptic operators in $\mathbb{R}^d$, $d=2,3$, with variable coefficients, which can be represented in a low rank separable form. We construct a…

The main challenge with the tensor completion problem is a fundamental tension between computation power and the information-theoretic sample complexity rate. Past approaches either achieve the information-theoretic rate but lack practical…

Modern biomedical studies often collect multi-view data, that is, multiple types of data measured on the same set of objects. A popular model in high-dimensional multi-view data analysis is to decompose each view's data matrix into a…