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An important problem in space-time adaptive detection is the estimation of the large p-by-p interference covariance matrix from training signals. When the number of training signals n is greater than 2p, existing estimators are generally…

Signal Processing · Electrical Eng. & Systems 2021-07-26 Benjamin D. Robinson , Robert Malinas , Alfred O. Hero

Balanced truncation is a well-established model order reduction method which has been applied to a variety of problems. Recently, a connection between linear Gaussian Bayesian inference problems and the system-theoretic concept of balanced…

Numerical Analysis · Mathematics 2024-01-04 Josie König , Melina A. Freitag

Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class…

Numerical Analysis · Mathematics 2015-12-22 John C. Urschel , Ludmil T. Zikatanov

A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is…

Computer Vision and Pattern Recognition · Computer Science 2015-05-27 Guoshen Yu , Guillermo Sapiro

Sampling theories lie at the heart of signal processing devices and communication systems. To accommodate high operating rates while retaining low computational cost, efficient analog-to digital (ADC) converters must be developed. Many of…

Information Theory · Computer Science 2010-10-12 Moslem Rashidi

Approximating the solution of the nonlinear filtering problem with Gaussian mixtures has been a very popular method since the 1970s. However, the vast majority of such approximations are introduced in an ad-hoc manner without theoretical…

Probability · Mathematics 2014-01-28 Dan Crisan , Kai Li

We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…

Applications · Statistics 2017-04-17 Guillaume Bouleux , Rémy Boyer

This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its…

Statistics Theory · Mathematics 2022-05-31 Victor Chernozhukov , Denis Chetverikov , Kengo Kato , Yuta Koike

We consider the problem of simulating a Gaussian vector X, conditional on the fact that each component of X belongs to a finite interval [a_i,b_i], or a semi-finite interval [a_i,+infty). In the one-dimensional case, we design a table-based…

Computation · Statistics 2012-01-31 Nicolas Chopin

Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…

Methodology · Statistics 2020-10-13 Yaniv Tenzer , Micha Mandel , Or Zuk

We investigate covariance shrinkage for Hotelling's $T^2$ in the regime where the data dimension $p$ and the sample size $n$ grow in a fixed ratio -- without assuming that the population covariance matrix is spiked or well-conditioned. When…

Statistics Theory · Mathematics 2025-06-13 Benjamin D. Robinson , Van Latimer

In this paper, we study the rate distortion function of the i.i.d sequence of multiplications of a Bernoulli $p$ random variable and a gaussian random variable $\sim N(0,1)$. We use a new technique in the derivation of the lower bound in…

Information Theory · Computer Science 2016-11-15 Cheng Chang

We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…

Machine Learning · Computer Science 2020-06-09 Ang Yang , Cheng Li , Santu Rana , Sunil Gupta , Svetha Venkatesh

We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…

Disordered Systems and Neural Networks · Physics 2025-11-17 Takashi Takahashi

We explore error distributions in Epoch of Reionization 21-cm power spectrum estimators using a combination of mathematical analysis and numerical simulations. We provide closed form solutions for the error distributions of individual bins…

Cosmology and Nongalactic Astrophysics · Physics 2023-04-20 Michael J. Wilensky , Jordan Brown , Bryna J. Hazelton

This paper addresses the reconstruction of sparse signals from generalized linear measurements. Signal sparsity is assumed to be sublinear in the signal dimension while it was proportional to the signal dimension in conventional research.…

Information Theory · Computer Science 2026-04-13 Keigo Takeuchi

In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant learning rate and study the explicit dependence of the convergence rate…

Machine Learning · Statistics 2025-09-18 Marat Khusainov , Marina Sheshukova , Alain Durmus , Sergey Samsonov

Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…

Classical Analysis and ODEs · Mathematics 2017-03-07 Stefan Lafon , Jacques Lévy Véhel , Jacques Peyrière

Consider the problem of detecting one of M i.i.d. Gaussian signals corrupted in white Gaussian noise. Conventionally, matched filters are used for detection. We first show that the outputs of the matched filter form a set of asymptotically…

Information Theory · Computer Science 2020-08-19 Jiachun Pan , Yonglong Li , Vincent Y. F. Tan , Yonina C. Eldar

Violation of the assumptions underlying classical (Gaussian) limit theory often yields unreliable statistical inference. This paper shows that the bootstrap can detect such violations by delivering simple and powerful diagnostic tests that…

Econometrics · Economics 2025-10-09 Giuseppe Cavaliere , Luca Fanelli , Iliyan Georgiev