Related papers: The Average Spectrum Norm and Near-Optimal Tensor …
Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…
DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of…
Low-Rank Tensor Completion, a method which exploits the inherent structure of tensors, has been studied extensively as an effective approach to tensor completion. Whilst such methods attained great success, none have systematically…
We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…
We show that the spectral norm of a random $n_1\times n_2\times \cdots \times n_K$ tensor (or higher-order array) scales as $O\left(\sqrt{(\sum_{k=1}^{K}n_k)\log(K)}\right)$ under some sub-Gaussian assumption on the entries. The proof is…
Real-world spatio-temporal data is often incomplete or inaccurate due to various data loading delays. For example, a location-disease-time tensor of case counts can have multiple delayed updates of recent temporal slices for some locations…
Matrix completion focuses on recovering missing or incomplete information in matrices. This problem arises in various applications, including image processing and network analysis. Previous research proposed Poisson matrix completion for…
Multi-relational learning has received lots of attention from researchers in various research communities. Most existing methods either suffer from superlinear per-iteration cost, or are sensitive to the given ranks. To address both issues,…
We establish several mathematical and computational properties of the nuclear norm for higher-order tensors. We show that like tensor rank, tensor nuclear norm is dependent on the choice of base field --- the value of the nuclear norm of a…
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…
We propose two provably accurate methods for low CP-rank tensor completion - one using adaptive sampling and one using nonadaptive sampling. Both of our algorithms combine matrix completion techniques for a small number of slices along with…
Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of the delicacy associated with the decomposition of higher order tensors. To…
This paper presents a Cramer-Rao lower bound (CRLB) on the variance of unbiased estimates of factor matrices in Canonical Polyadic (CP) or CANDECOMP/PARAFAC (CP) decompositions of a tensor from noisy observations, (i.e., the tensor plus a…
This paper presents a novel power spectral density estimation technique for band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The technique employs multi-coset sampling and incorporates the advantages of compressed…
Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing…
The line spectral estimation problem consists in recovering the frequencies of a complex valued time signal that is assumed to be sparse in the spectral domain from its discrete observations. Unlike the gridding required by the classical…
Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…
In real-world scenarios, spatiotemporal traffic data frequently experiences dual degradation from missing values and noise caused by sensor malfunctions and communication failures. Therefore, effective data recovery methods are essential to…
We give a spectral algorithm for decomposing overcomplete order-4 tensors, so long as their components satisfy an algebraic non-degeneracy condition that holds for nearly all (all but an algebraic set of measure $0$) tensors over…
We study the computational properties of two canonical planted average-case problems -- noisy planted $k$-XOR and Tensor PCA -- by formally unifying them into a family of planted problems parametrized by tensor order $k$, number of entries…