Related papers: Threshold Tensor Factor Model in CP Form

Integrated sensing and communications (ISAC) is a key use case for sixth-generation (6G) wireless systems, where parametric channel estimation (PCE) plays a central role in enabling sensing, localization, and channel equalization in…

Canonical Polyadic Decomposition (CPD) of a third-order tensor is a minimal decomposition into a sum of rank-$1$ tensors. We find new mild deterministic conditions for the uniqueness of individual rank-$1$ tensors in CPD and present an…

Several approaches for predicting large volatility matrices have been developed based on high-dimensional factor-based It\^o processes. These methods often impose restrictions to reduce the model complexity, such as constant eigenvectors or…

Tensor PCA is a stylized statistical inference problem introduced by Montanari and Richard to study the computational difficulty of estimating an unknown parameter from higher-order moment tensors. Unlike its matrix counterpart, Tensor PCA…

This paper develops a novel method to estimate a latent factor model for a large target panel with missing observations by optimally using the information from auxiliary panel data sets. We refer to our estimator as target-PCA. Transfer…

Because of the attractiveness of the canonical polyadic (CP) tensor decomposition in various applications, several algorithms have been designed to compute it, but efficient ones are still lacking. Iterative deflation algorithms based on…

Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT)…

The letter proposes an adaptive model reduction approach based on tensor decomposition to speed up time-domain power system simulation. Taylor series expansion of a power system dynamic model is calculated around multiple equilibria…

In this paper, we use the time super-operator formalism in the 2-level Friedrichs model \cite{fried} to obtain a phenomenological model of mesons decay. Our approach provides a fairly good estimation of the CP symmetry violation parameter…

CP decomposition is a powerful tool for data science, especially gene analysis, deep learning, and quantum computation. However, the application of tensor decomposition is largely hindered by the exponential increment of the computational…

Tensors have broad applications in neuroimaging, data mining, digital marketing, etc. CANDECOMP/PARAFAC (CP) tensor decomposition can effectively reduce the number of parameters to gain dimensionality-reduction and thus plays a key role in…

The recent low-rank prior based models solve the tensor completion problem efficiently. However, these models fail to exploit the local patterns of tensors, which compromises the performance of tensor completion. In this paper, we propose a…

This paper introduces a general framework of Semi-parametric TEnsor Factor Analysis (STEFA) that focuses on the methodology and theory of low-rank tensor decomposition with auxiliary covariates. Semi-parametric TEnsor Factor Analysis models…

Dimensionality reduction for high-order tensors is a challenging problem. In conventional approaches, higher order tensors are `vectorized` via Tucker decomposition to obtain lower order tensors. This will destroy the inherent high-order…

We address prediction problems on tabular categorical data, where each instance is defined by multiple categorical attributes, each taking values from a finite set. These attributes are often referred to as fields, and their categorical…

Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis,…

We consider sequential state and parameter learning in state-space models with intractable state transition and observation processes. By exploiting low-rank tensor train (TT) decompositions, we propose new sequential learning methods for…

Tensor networks have a gauge degree of freedom on the virtual degrees of freedom that are contracted. A canonical form is a choice of fixing this degree of freedom. For matrix product states, choosing a canonical form is a powerful tool,…

Task-evoked functional magnetic resonance imaging studies, such as the Human Connectome Project (HCP), are a powerful tool for exploring how brain activity is influenced by cognitive tasks like memory retention, decision-making, and…

Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)---amount to multi-linear factorization. They are…