Related papers: QUARKS: Identification of large-scale Kronecker Ve…
Tensor Kronecker products, the natural generalization of the matrix Kronecker product, are independently emerging in multiple research communities. Like their matrix counterpart, the tensor generalization gives structure for implicit…
Kronecker product covariance structure provides an efficient way to modeling the inter-correlations of matrix-variate data. In this paper, we propose testing statistics for Kronecker product covariance matrix based on linear spectral…
This paper derives sufficient conditions for local recovery of coordinate dictionaries comprising a Kronecker-structured dictionary that is used for representing $K$th-order tensor data. Tensor observations are assumed to be generated from…
This paper studies the problem of Kronecker-structured sparse vector recovery from an underdetermined linear system with a Kronecker-structured dictionary. Such a problem arises in many real-world applications such as the sparse channel…
Reduced-rank regressions are powerful tools used to identify co-movements within economic time series. However, this task becomes challenging when we observe matrix-valued time series, where each dimension may have a different co-movement…
Autoregressive networks can achieve promising performance in many sequence modeling tasks with short-range dependence. However, when handling high-dimensional inputs and outputs, the huge amount of parameters in the network lead to…
Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper…
In recent years, a class of dictionaries have been proposed for multidimensional (tensor) data representation that exploit the structure of tensor data by imposing a Kronecker structure on the dictionary underlying the data. In this work, a…
Our work addresses two important issues with recurrent neural networks: (1) they are over-parameterized, and (2) the recurrence matrix is ill-conditioned. The former increases the sample complexity of learning and the training time. The…
Deep learning using neural networks is an effective technique for generating models of complex data. However, training such models can be expensive when networks have large model capacity resulting from a large number of layers and nodes.…
We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block-banded), or be more highly structured (e.g., symmetric…
This paper introduces a matrix-variate regression model for analyzing multivariate data observed across spatial locations and over time. The model's design incorporates a mean structure that links covariates to the response matrix and a…
We propose a new class of spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a sparse structure for high-dimensional spatial panel dynamic models when panel members represent economic…
We study the computational model where we can access a matrix $\mathbf{A}$ only by computing matrix-vector products $\mathbf{A}\mathrm{x}$ for vectors of the form $\mathrm{x} = \mathrm{x}_1 \otimes \cdots \otimes \mathrm{x}_q$. We prove…
Hypergraphs and tensors extend classic graph and matrix theory to account for multiway relationships, which are ubiquitous in engineering, biological, and social systems. While the Kronecker product is a potent tool for analyzing the…
Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class…
The Kronecker product is an invaluable tool for data-sparse representations of large networks and matrices with countless applications in machine learning, graph theory and numerical linear algebra. In some instances, the sparsity pattern…
How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and…
We develop a parametric high-resolution method for the estimation of the frequency nodes of linear combinations of complex exponentials with exponential damping. We use Kronecker's theorem to formulate the associated nonlinear least squares…
The starting point for this work is an identity that relates the number of minimal matrices with prescribed 1-marginals and coefficient sequence to a linear combination of Kronecker coefficients. In this paper we provide a bijection that…