Related papers: Interpolating Convex and Non-Convex Tensor Decompo…

Noisy $k$-XOR is a basic average-case inference problem in which one observes random noisy $k$-ary parity constraints and seeks to recover, or more weakly, detect, a hidden Boolean assignment. A central question is to characterize the…

We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and…

We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…

We give constructions of n^k x n^k x n tensors of rank at least 2n^k - O(n^(k-1)). As a corollary we obtain an [n]^r shaped tensor with rank at least 2n^(r/2) - O(n^(r/2)-1) when r is odd. The tensors are constructed from a simple recursive…

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…

It is well-known that point sources with sufficient mutual distance can be reconstructed exactly from finitely many Fourier measurements by solving a convex optimization problem with Tikhonov-regularization (this property is sometimes…

In this paper we generalize the 1-bit matrix completion problem to higher order tensors. We prove that when $r=O(1)$ a bounded rank-$r$, order-$d$ tensor $T$ in $\mathbb{R}^{N} \times \mathbb{R}^{N} \times \cdots \times \mathbb{R}^{N}$ can…

We provide guarantees for learning latent variable models emphasizing on the overcomplete regime, where the dimensionality of the latent space can exceed the observed dimensionality. In particular, we consider multiview mixtures, spherical…

Currently, low-rank tensor completion has gained cumulative attention in recovering incomplete visual data whose partial elements are missing. By taking a color image or video as a three-dimensional (3D) tensor, previous studies have…

This paper considers approximately sparse signal and low-rank matrix's recovery via truncated norm minimization $\min_{x}\|x_T\|_q$ and $\min_{X}\|X_T\|_{S_q}$ from noisy measurements. We first introduce truncated sparse approximation…

Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…

Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…

Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…

We present an algorithm for low rank decomposition of tensors of any symmetry type, from fully asymmetric to fully symmetric. It recovers the decomposition one summand at a time via the higher-order power method. This approach is known to…

Recovering a low-CP-rank tensor from noisy linear measurements is a central challenge in high-dimensional data analysis, with applications spanning tensor PCA, tensor regression, and beyond. We exploit the intrinsic geometry of rank-one…

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

We consider the problem of detecting whether a tensor signal having many missing entities lies within a given low dimensional Kronecker-Structured (KS) subspace. This is a matched subspace detection problem. Tensor matched subspace…

We proposed a weighted l1 minimization to recover a sparse signal vector and the corrupted noise vector from a linear measurement when the sensing matrix A is an m by n row i.i.d subgaussian matrix. We obtain both uniform and nonuniform…

We study low rank approximation of tensors, focusing on the tensor train and Tucker decompositions, as well as approximations with tree tensor networks and more general tensor networks. For tensor train decomposition, we give a bicriteria…

In compressed sensing one uses known structures of otherwise unknown signals to recover them from as few linear observations as possible. The structure comes in form of some compressibility including different notions of sparsity and low…