Related papers: Detection of Signal in the Spiked Rectangular Mode…
This paper considers the problems of detecting a change point and estimating the location in the correlation matrices of a sequence of high-dimensional vectors, where the dimension is large enough to be comparable to the sample size or even…
Sparse linear regression is one of the most basic questions in machine learning and statistics. Here, we are given as input a design matrix $X \in \mathbb{R}^{N \times d}$ and measurements or labels ${y} \in \mathbb{R}^N$ where ${y} = {X}…
The recent development of compressed sensing has led to spectacular advances in the understanding of sparse linear estimation problems as well as in algorithms to solve them. It has also triggered a new wave of developments in the related…
Matched filtering is a long-standing technique for the optimal detection of known signals in stationary Gaussian noise. However, it has known departures from optimality when operating on unknown signals in real noise and suffers from…
It is expected that gravitational waves, similar to electromagnetic waves, can be gravitationally lensed by intervening matters, producing multiple instances of the same signal arriving at different times from different apparent luminosity…
This study proposes a novel hierarchical prior for inferring possibly low-rank matrices measured with noise. We consider three-component matrix factorization, as in singular value decomposition, and its fully Bayesian inference. The…
We describe several new techniques which accelerate Bayesian searches for continuous gravitational-wave emission from supermassive black-hole binaries using pulsar timing arrays. These techniques mitigate the problematic increase of…
Theories with more than one scalar field often exhibit phase transitions producing potentially detectable gravitational wave (GW) signal. In this work we study the semi-annihilating $\mathbb{Z}_3$ dark matter model, whose dark sector…
Given $p$-dimensional Gaussian vectors $X_i \stackrel{iid}{\sim} N(0, \Sigma)$, $1 \leq i \leq n$, where $p \geq n$, we are interested in testing a null hypothesis where $\Sigma = I_p$ against an alternative hypothesis where all eigenvalues…
We study the problem of detection of a p-dimensional sparse vector of parameters in the linear regression model with Gaussian noise. We establish the detection boundary, i.e., the necessary and sufficient conditions for the possibility of…
We introduce a novel class of Bayesian mixtures for normal linear regression models which incorporates a further Gaussian random component for the distribution of the predictor variables. The proposed cluster-weighted model aims to…
Gravitational-wave (GW) parameter estimation typically assumes that instrumental noise is Gaussian and stationary. Obvious departures from this idealization are typically handled on a case-by-case basis, e.g., through bespoke procedures to…
We study information-theoretic phase transitions for the detectability of latent geometry in bipartite random geometric graphs RGGs with Gaussian d-dimensional latent vectors while only a subset of edges carries latent information…
Testing for white noise is a classical yet important problem in statistics, especially for diagnostic checks in time series modeling and linear regression. For high-dimensional time series in the sense that the dimension $p$ is large in…
With the significantly improved sensitivity and a wider frequency band, the next-generation gravitational-wave (GW) detectors are anticipated to detect $\sim 10^5$ GW signals per year with durations from hours to days, leading to inevitable…
The Gaussian phase noise of intensity time series is demonstrated to be drastically reduced when the raw voltage data are digitally filtered through an arbitrarily large number $n$ of orthornormal bandpass profiles (eigen-filters) sharing…
Discovering governing equations from data is important to many scientific and engineering applications. Despite promising successes, existing methods are still challenged by data sparsity and noise issues, both of which are ubiquitous in…
Given a large, high-dimensional sample from a spiked population, the top sample covariance eigenvalue is known to exhibit a phase transition. We show that the largest eigenvalues have asymptotic distributions near the phase transition in…
We study high-dimensional regression in principal components space when the predictors are observed with additive measurement error and the response errors may be heavy-tailed. The starting point is the $\ell_1$-penalized…
Consider the problem of estimating a low-rank matrix when its entries are perturbed by Gaussian noise. If the empirical distribution of the entries of the spikes is known, optimal estimators that exploit this knowledge can substantially…