Related papers: Statistical Limits in Random Tensors with Multiple…

We study the statistical limits of testing and estimation for a rank one deformation of a Gaussian random tensor. We compute the sharp thresholds for hypothesis testing and estimation by maximum likelihood and show that they are the same.…

Consider a spiked random tensor obtained as a mixture of two components: noise in the form of a symmetric Gaussian $p$-tensor for $p\geq 3$ and signal in the form of a symmetric low-rank random tensor. The latter is defined as a linear…

Relying on random matrix theory (RMT), this paper studies asymmetric order-$d$ spiked tensor models with Gaussian noise. Using the variational definition of the singular vectors and values of (Lim, 2005), we show that the analysis of the…

We study asymmetric rank-one spiked tensor models in the high-dimensional regime, where the noise entries are independent and identically distributed with zero mean, unit variance, and finite fourth moment. This extends the classical…

We study the statistical limits of both detecting and estimating a rank-one deformation of a symmetric random Gaussian tensor. We establish upper and lower bounds on the critical signal-to-noise ratio, under a variety of priors for the…

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…

We consider the problem of estimating a large rank-one tensor ${\boldsymbol u}^{\otimes k}\in({\mathbb R}^{n})^{\otimes k}$, $k\ge 3$ in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio $\lambda_{Bayes}= O(1)$…

We study the fundamental limits of detecting the presence of an additive rank-one perturbation, or spike, to a Wigner matrix. When the spike comes from a prior that is i.i.d. across coordinates, we prove that the log-likelihood ratio of the…

This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered…

We consider rank-one symmetric tensor estimation when the tensor is corrupted by Gaussian noise and the spike forming the tensor is a structured signal coming from a generalized linear model. The latter is a mathematically tractable model…

The top eigenvalues of rank $r$ spiked real Wishart matrices and additively perturbed Gaussian orthogonal ensembles are known to exhibit a phase transition in the large size limit. We show that they have limiting distributions for…

In this paper, we study the power iteration algorithm for the spiked tensor model, as introduced in [44]. We give necessary and sufficient conditions for the convergence of the power iteration algorithm. When the power iteration algorithm…

We study here the so-called spiked Wigner and Wishart models, where one observes a low-rank matrix perturbed by some Gaussian noise. These models encompass many classical statistical tasks such as sparse PCA, submatrix localization,…

In this paper, we consider the singular values and singular vectors of low rank perturbations of large rectangular random matrices, in the regime the matrix is "long": we allow the number of rows (columns) to grow polynomially in the number…

In this paper, we study the estimation of a rank-one spiked tensor in the presence of heavy tailed noise. Our results highlight some of the fundamental similarities and differences in the tradeoff between statistical and computational…

Generalized Linear Models (GLMs) have been used extensively in statistical models of spike train data. However, the maximum likelihood estimates of the model parameters and their uncertainty, can be challenging to compute in situations…

We study the statistical decision process of detecting the low-rank signal from various signal-plus-noise type data matrices, known as the spiked random matrix models. We first show that the principal component analysis can be improved by…

In this paper, we derive results about the limiting distribution of the empirical magnetization vector and the maximum likelihood (ML) estimates of the natural parameters in the tensor Curie-Weiss Potts model. Our results reveal…

We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…

This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…