Related papers: Computational and Statistical Boundaries for Subma…
This paper studies the minimax detection of a small submatrix of elevated mean in a large matrix contaminated by additive Gaussian noise. To investigate the tradeoff between statistical performance and computational cost from a…
In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…
We consider a group synchronization problem with multiple frequencies which involves observing pairwise relative measurements of group elements on multiple frequency channels, corrupted by Gaussian noise. We study the computational phase…
We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…
This paper investigates the fundamental limits for detecting a high-dimensional sparse matrix contaminated by white Gaussian noise from both the statistical and computational perspectives. We consider $p\times p$ matrices whose rows and…
We consider the problem of localizing a submatrix with larger-than-usual entry values inside a data matrix, without the prior knowledge of the submatrix size. We establish an optimization framework based on a multiscale scan statistic, and…
We consider two closely related problems: planted clustering and submatrix localization. The planted clustering problem assumes that a random graph is generated based on some underlying clusters of the nodes; the task is to recover these…
The principal submatrix localization problem deals with recovering a $K\times K$ principal submatrix of elevated mean $\mu$ in a large $n\times n$ symmetric matrix subject to additive standard Gaussian noise. This problem serves as a…
Locating a target is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In scenarios where precise statistics of the measurement noise are unavailable,…
We study the computational phase transition in a multi-frequency group synchronization problem, where pairwise relative measurements of group elements are observed across multiple frequency channels and corrupted by Gaussian noise. Using…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…
We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and submatrix localization. Each of these problems is…
Structural matrix-variate observations routinely arise in diverse fields such as multi-layer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the…
Over the past few years, insights from computer science, statistical physics, and information theory have revealed phase transitions in a wide array of high-dimensional statistical problems at two distinct thresholds: One is the…
Recent work has generalized several results concerning the well-understood spiked Wigner matrix model of a low-rank signal matrix corrupted by additive i.i.d. Gaussian noise to the inhomogeneous case, where the noise has a variance profile.…
The aim of this Lecture Note is to introduce the Signal Processing (SP) community to a powerful yet still under-utilised tool: the semiparametric statistics. In short, the semiparametric framework allows us to estimate or perform hypothesis…
Spike train signals recorded from a large population of neurons often exhibit low-dimensional spatio-temporal structure and modeled as conditional Poisson observations. The low-dimensional signals that capture internal brain states are…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…