Related papers: On the Accuracy of Hotelling-Type Tensor Deflation…

The recent BICEP2 B-mode polarization determination of an inflationary tensor-scalar ratio $r=0.2^{+0.07}_{-0.05}$ is in tension with simple scale-free models of inflation due to a lack of a corresponding low multipole excess in the…

Thanks to their high quality, new and upcoming asteroseismic observations - with CoRoT, Kepler, and from the ground... - can benefit from the experience gained with helioseismology. We focus in this paper on solar-like oscillations, for…

We investigate the possibility of inflation with models of antisymmetric tensor field having minimal and nonminimal couplings to gravity. Although the minimal model does not support inflation, the nonminimal models, through the introduction…

In this paper, we develop novel perturbation bounds for the high-order orthogonal iteration (HOOI) [DLDMV00b]. Under mild regularity conditions, we establish blockwise tensor perturbation bounds for HOOI with guarantees for both tensor…

Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…

Statistical inference for tensors has emerged as a critical challenge in analyzing high-dimensional data in modern data science. This paper introduces a unified framework for inferring general and low-Tucker-rank linear functionals of…

Efficient and accurate low-rank approximation (LRA) methods are of great significance for large-scale data analysis. Randomized tensor decompositions have emerged as powerful tools to meet this need, but most existing methods perform poorly…

This paper establishes new restricted isometry conditions for compressed sensing and affine rank minimization. It is shown for compressed sensing that $\delta_{k}^A+\theta_{k,k}^A < 1$ guarantees the exact recovery of all $k$ sparse signals…

We consider properties of determinants of some random symmetric matrices issued from multivariate statistics: Wishart/Laguerre ensemble (sample covariance matrices), Uniform Gram ensemble (sample correlation matrices) and Jacobi ensemble…

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…

One-rank perturbations of Wigner matrices have been closely studied: let $P=\frac{1}{\sqrt{n}}A+\theta vv^T$ with $A=(a_{ij})_{1 \leq i,j \leq n} \in \mathbb{R}^{n \times n}$ symmetric, $(a_{ij})_{1 \leq i \leq j \leq n}$ i.i.d. with…

This paper studies the issues about tensors. Three typical kinds of tensor decomposition are mentioned. Among these decompositions, the t-SVD is proposed in this decade. Different definitions of rank derive from tensor decompositions. Based…

Consider large signal-plus-noise data matrices of the form $S + \Sigma^{1/2} X$, where $S$ is a low-rank deterministic signal matrix and the noise covariance matrix $\Sigma$ can be anisotropic. We establish the asymptotic joint distribution…

Many applications involve estimation of a signal matrix from a noisy data matrix. In such cases, it has been observed that estimators that shrink or truncate the singular values of the data matrix perform well when the signal matrix has…

This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…

The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…

This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\mathbf{M}^{\star}\in \mathbb{R}^{n\times n}$, yet only a randomly…

We prove a non-asymptotic concentration inequality for the spectral norm of sparse inhomogeneous random tensors with Bernoulli entries. For an order-$k$ inhomogeneous random tensor $T$ with sparsity $p_{\max}\geq \frac{c\log n}{n }$, we…

The $k$-tensor Ising model is an exponential family on a $p$-dimensional binary hypercube for modeling dependent binary data, where the sufficient statistic consists of all $k$-fold products of the observations, and the parameter is an…

Tensor time series data appears naturally in a lot of fields, including finance and economics. As a major dimension reduction tool, similar to its factor model counterpart, the idiosyncratic components of a tensor time series factor model…