Related papers: On Testing Kronecker Product Structure in Tensor F…
We propose a test for a covariance matrix to have Kronecker Product Structure (KPS). KPS implies a reduced rank restriction on a certain transformation of the covariance matrix and the new procedure is an adaptation of the Kleibergen and…
Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…
We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…
We obtain several rigidity results regarding tensor product decompositions of factors. First, we show that any full factor with separable predual has at most countably many tensor product decompositions up to stable unitary conjugacy. We…
We develop a higher order generalization of the LQ decomposition and show that this decomposition plays an important role in likelihood-based estimation and testing for separable, or Kronecker structured, covariance models, such as the…
We study the matrix-variate regression problem $Y_i = \sum_{k} \beta_{1k} X_i \beta_{2k}^{\top} + E_i$ for $i=1,2\dots,n$ in the high dimensional regime wherein the response $Y_i$ are matrices whose dimensions $p_{1}\times p_{2}$ outgrow…
Over the real numbers, the Kronecker sum is the unique operation on matrices which exponentiates to the Kronecker product. Kronecker quotients provide an algebraic view of decompositions of matrices in terms of Kronecker products. This…
The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…
Portfolio allocation and risk management make use of correlation matrices and heavily rely on the choice of a proper correlation matrix to be used. In this regard, one important question is related to the choice of the proper sample period…
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 reduced Kronecker coefficients are particular instances of Kronecker coefficients that contain enough information to recover them. In this notes we compute the generating function of a family of reduced Kronecker coefficients. We also…
The properties and applications of kronecker product in quantum theory is studied thoroughly. The use of kronecker product in quantum information theory to get the exact spin Hamiltonian is given. The proof of non-commutativity of matrices,…
Kronecker adapters have emerged as a promising approach for fine-tuning large-scale models, enabling high-rank updates through tunable component structures. However, existing work largely treats the component structure as a fixed or…
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…
Longitudinal imaging studies have moved to the forefront of medical research due to their ability to characterize spatio-temporal features of biological structures across the lifespan. Credible models of the correlations in longitudinal…
Contingency table analysis routinely relies on log linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a low rank tensor factorization of the probability mass function for…
Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…
The Kronecker product is a key algorithm and is ubiquitous across the physical, biological, and computation social sciences. Thus considerations of optimal implementation are important. The need to have high performance and computational…
We propose an adjusted likelihood ratio test of two-factor separability (Kronecker product structure) for unbalanced multivariate repeated measures data. Here we address the particular case where the within subject correlation is believed…
High-dimensional, higher-order tensor data are gaining prominence in a variety of fields, including but not limited to computer vision and network analysis. Tensor factor models, induced from noisy versions of tensor decompositions or…