Related papers: Tensor-based Model Reduction and Identification fo…

Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems…

Sparse tensors are the most used representation of sparse multidimensional data. Operations that decompose them, selecting their most important features while reducing their dimension, have become prevalent procedures in machine learning.…

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 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…

There have been many attempts to identify high-dimensional network features via multivariate approaches. Specifically, when the number of voxels or nodes, denoted as p, are substantially larger than the number of images, denoted as n, it…

Recently it has been shown that tensor networks (TNs) have the ability to represent the expected return of a single-agent finite Markov decision process (FMDP). The TN represents a distribution model, where all possible trajectories are…

In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…

Homogeneous polynomial dynamical systems (HPDSs), which can be equivalently represented by tensors, are essential for modeling higher-order networked systems, including ecological networks, chemical reactions, and multi-agent robotic…

Compressed sensing (CS) exploits the sparsity of a signal in order to integrate acquisition and compression. CS theory enables exact reconstruction of a sparse signal from relatively few linear measurements via a suitable nonlinear…

Researchers are increasingly incorporating numeric high-order data, i.e., numeric tensors, within their practice. Just like the matrix/vector (MV) paradigm, the development of multi-purpose, but high-performance, sparse data structures and…

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…

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…

Model reduction plays a critical role in system control, with established methods such as balanced truncation widely used for linear systems. However, extending these methods to nonlinear settings, particularly polynomial dynamical systems…

It is of great significance to apply deep learning for the early diagnosis of Alzheimer's Disease (AD). In this work, a novel tensorizing GAN with high-order pooling is proposed to assess Mild Cognitive Impairment (MCI) and AD. By…

Neural networks equipped with self-attention have parallelizable computation, light-weight structure, and the ability to capture both long-range and local dependencies. Further, their expressive power and performance can be boosted by using…

Automatic Modulation Recognition (AMR) plays a crucial role in wireless communication systems. Deep learning AMR strategies have achieved tremendous success in recent years. Modulated signals exhibit long temporal dependencies, and…

This paper proposes a tensor-based parametric modeling and estimation framework in multiple-input multiple-output (MIMO) systems assisted by intelligent reflecting surfaces (IRSs). We present two algorithms that exploit the tensor structure…

The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to…

Recent years have demonstrated that using random feature maps can significantly decrease the training and testing times of kernel-based algorithms without significantly lowering their accuracy. Regrettably, because random features are…

This paper proposes a tensor-based parameter estimation algorithm for sensing in an intelligent reflecting surface-assisted system. We present a higher-order singular value decomposition-based solution that exploits the tensor structure of…