Related papers: Statistical limits of spiked tensor models

In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…

The goal of this paper is to characterize the best achievable performance for the problem of estimating an unknown parameter having a sparse representation. Specifically, we consider the setting in which a sparsely representable…

Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…

We study the tensor-on-tensor regression, where the goal is to connect tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without the prior knowledge of its intrinsic rank. We propose the Riemannian…

The estimation of parameters characterizing dynamical processes is central to science and technology. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of…

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…

The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…

Tensor-based modulation (TBM) has been proposed in the context of unsourced random access for massive uplink communication. In this modulation, transmitters encode data as rank-1 tensors, with factors from a discrete vector constellation.…

The ultimate sensitivity of optical detection is limited by the signal-to-noise ratio (SNR). The first part of the paper shows that coherence plays an important role in the noise analysis. Although interference between an auxiliary wave and…

We establish maximal concentration bounds for the iterates generated by stochastic approximation algorithms with general step sizes, where the noise has a finite-state Markovian component plus a Martingale-difference component. When the…

This article develops limit laws for network sampling based estimates of subgraph counts and clustering coefficient of a large population network, and uses them for predictive inference. A model based approach is used, where the population…

Consider the standard Gaussian linear regression model $Y=X\theta+\epsilon$, where $Y\in R^n$ is a response vector and $ X\in R^{n*p}$ is a design matrix. Numerous work have been devoted to building efficient estimators of $\theta$ when $p$…

We study the high-dimensional dynamics of online stochastic gradient descent (SGD) for the multi-spiked tensor model. This multi-index model arises from the tensor principal component analysis (PCA) problem with multiple spikes, where the…

We consider entanglement-assisted frequency estimation by Ramsey interferometry, in the presence of dephasing noise from spatiotemporally correlated environments.By working in the widely employed local estimation regime, we show that even…

We propose a nonparametric factorization approach for sparsely observed tensors. The sparsity does not mean zero-valued entries are massive or dominated. Rather, it implies the observed entries are very few, and even fewer with the growth…

Restricted Isometry Property (RIP) is of fundamental importance in the theory of compressed sensing and forms the base of many exact and robust recovery guarantees in this field. A quantitative description of RIP involves bounding the…

Robust estimation is an important and timely research subject. In this paper, we investigate performance lower bounds on the mean-square-error (MSE) of any estimator for the Bayesian linear model, corrupted by a noise distributed according…

In the Tensor PCA problem introduced by Richard and Montanari (2014), one is given a dataset consisting of $n$ samples $\mathbf{T}_{1:n}$ of i.i.d. Gaussian tensors of order $k$ with the promise that $\mathbb{E}\mathbf{T}_1$ is a rank-1…

Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…

This paper develops theoretical results regarding noisy 1-bit compressed sensing and sparse binomial regression. We show that a single convex program gives an accurate estimate of the signal, or coefficient vector, for both of these models.…