Related papers: Improving tensor regression by optimal model avera…

In general, algorithms for order-3 CANDECOMP/-PARAFAC (CP), also coined canonical polyadic decomposition (CPD), are easily to implement and can be extended to higher order CPD. Unfortunately, the algorithms become computationally demanding,…

Most regularized tensor regression research focuses on tensors predictors with scalars responses or vectors predictors to tensors responses. We consider the sparse low rank tensor on tensor regression where predictors $\mathcal{X}$ and…

The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…

Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…

Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in…

Canonical Polyadic (or CANDECOMP/PARAFAC, CP) decompositions (CPD) are widely applied to analyze high order tensors. Existing CPD methods use alternating least square (ALS) iterations and hence need to unfold tensors to each of the $N$…

We establish non-asymptotic efficiency guarantees for tensor decomposition-based inference in count data models. Under a Poisson framework, we consider two related goals: (i) parametric inference, the estimation of the full distributional…

The CANDECOMP/PARAFAC (CP) decomposition is a generalization of the spectral decomposition of matrices to higher-order tensors. In this paper we use the CP decomposition to study unitary equivalence of higher order tensors and construct…

High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include…

High-dimensional tensor-valued predictors arise in modern applications, increasingly as learned representations from neural networks. Existing tensor classification methods rely on sparsity or Tucker structures and often lack theoretical…

In many high-dimensional estimation problems the main task consists in minimizing a cost function, which is often strongly non-convex when scanned in the space of parameters to be estimated. A standard solution to flatten the corresponding…

Tensor-valued data are becoming increasingly available in economics and this calls for suitable econometric tools. We propose a new dynamic linear model for tensor-valued response variables and covariates that encompasses some well-known…

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…

CANDECOMP/PARAFAC (CP) decomposition has been widely used to deal with multi-way data. For real-time or large-scale tensors, based on the ideas of randomized-sampling CP decomposition algorithm and online CP decomposition algorithm, a novel…

This paper explores a new version of the Levenberg-Marquardt algorithm used for Tensor Canonical Polyadic (CP) decomposition with an emphasis on image compression and reconstruction. Tensor computation, especially CP decomposition, holds…

Fabrication process variations can significantly influence the performance and yield of nano-scale electronic and photonic circuits. Stochastic spectral methods have achieved great success in quantifying the impact of process variations,…

Canonical Polyadic (CP) tensor decomposition is a fundamental technique for analyzing high-dimensional tensor data. While the Alternating Least Squares (ALS) algorithm is widely used for computing CP decomposition due to its simplicity and…

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…

All neuroimaging modalities have their own strengths and limitations. A current trend is toward interdisciplinary approaches that use multiple imaging methods to overcome limitations of each method in isolation. At the same time…

CANDECOMP/PARAFAC (CP) decomposition is the mostly used model to formulate the received tensor signal in a massive MIMO system, as the receiver generally sums the components from different paths or users. To achieve accurate and low-latency…