English
Related papers

Related papers: Extreme value theory for singular subspace estimat…

200 papers

We present a study of the numerical solution of the two dimensional electrical impedance tomography problem, with noisy measurements of the Dirichlet to Neumann map. The inversion uses parametrizations of the conductivity on optimal grids.…

Mathematical Physics · Physics 2015-06-03 Liliana Borcea , Fernando Guevara Vasquez , Alexander V. Mamonov

We consider the task of estimating a low-rank matrix from non-linear and noisy observations. We prove a strong universality result showing that Bayes-optimal performances are characterized by an equivalent Gaussian model with an effective…

Machine Learning · Statistics 2024-03-08 Pierre Mergny , Justin Ko , Florent Krzakala , Lenka Zdeborová

We study symmetric spiked matrix models with respect to a general class of noise distributions. Given a rank-1 deformation of a random noise matrix, whose entries are independently distributed with zero mean and unit variance, the goal is…

Data Structures and Algorithms · Computer Science 2022-02-22 Jingqiu Ding , Samuel B. Hopkins , David Steurer

In contrast to multi-label learning, label distribution learning characterizes the polysemy of examples by a label distribution to represent richer semantics. In the learning process of label distribution, the training data is collected…

Machine Learning · Computer Science 2022-09-29 Zhuoran Zheng , Xiuyi Jia

Extreme value theory for chaotic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory studies the limit probabilistic laws obeyed by…

Dynamical Systems · Mathematics 2015-05-28 Mark P. Holland , Renato Vitolo , Pau Rabassa , Alef E. Sterk , Henk W. Broer

Spectral methods are widely used to estimate eigenvectors of a low-rank signal matrix subject to noise. These methods use the leading eigenspace of an observed matrix to estimate this low-rank signal. Typically, the entrywise estimation…

Statistics Theory · Mathematics 2024-11-01 Hao Yan , Keith Levin

We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…

Methodology · Statistics 2014-02-05 Adel Javanmard , Andrea Montanari

The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the…

Machine Learning · Statistics 2017-04-26 Ashwin Pananjady , Martin J. Wainwright , Thomas A. Courtade

This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…

Statistics Theory · Mathematics 2019-03-18 Dominique Dehay , Khalil El Waled , Vincent Monsan

In this note we obtain tight bounds on the space-complexity of computing the ergodic measure of a low-dimensional discrete-time dynamical system affected by Gaussian noise. If the scale of the noise is $\varepsilon$, and the function…

Computational Complexity · Computer Science 2015-08-24 Mark Braverman , Cristobal Rojas , Jon Schneider

We consider Bayesian multiple statistical classification problem in the case where the unknown source distributions are estimated from the labeled training sequences, then the estimates are used as nominal distributions in a robust…

Information Theory · Computer Science 2021-10-11 Hüseyin Afşer

This article concerns the non-asymptotic analysis of the singular values (and Lyapunov exponents) of Gaussian matrix products in the regime where $N,$ the number of term in the product, is large and $n,$ the size of the matrices, may be…

Probability · Mathematics 2021-03-24 Boris Hanin , Grigoris Paouris

We consider the problem of sparse normal means estimation in a distributed setting with communication constraints. We assume there are $M$ machines, each holding $d$-dimensional observations of a $K$-sparse vector $\mu$ corrupted by…

Machine Learning · Statistics 2022-02-15 Chen Amiraz , Robert Krauthgamer , Boaz Nadler

In this paper we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the robustness property against erasure for the almost norm preservation property of…

Information Theory · Computer Science 2015-01-09 Bin Han , Zhiqiang Xu

We quantify the large deviations of Gaussian extreme value statistics on closed convex sets in d-dimensional Euclidean space. The asymptotics imply that the extreme value distribution exhibits a rate function that is a simple quadratic…

Probability · Mathematics 2018-10-31 Harsha Honnappa , Raghu Pasupathy , Prateek Jaiswal

For a class of idealized chaotic systems (hyperbolic systems) correlations decay exponentially in time. This result is asymptotic and rigorous. The decay rate is related to the Ruelle-Pollicott resonances. Nearly all chaotic model systems,…

Chaotic Dynamics · Physics 2007-05-23 Shmuel Fishman , Saar Rahav

In the inverse Gaussian sequence space model with additional noisy observations of the operator, we derive nonasymptotic minimax radii of testing for ellipsoid-type alternatives simultaneously for both the signal detection problem (testing…

Statistics Theory · Mathematics 2020-02-19 Sandra Schluttenhofer , Jan Johannes

We consider a finite horizon linear discrete time varying system whose input is a random noise with an imprecisely known probability law. The statistical uncertainty is described by a nonnegative parameter a which constrains the anisotropy…

Systems and Control · Computer Science 2012-08-21 Eugene A. Maximov , Alexander P. Kurdyukov , Igor G. Vladimirov

We consider the high-dimensional inference problem where the signal is a low-rank matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large dimension…

Probability · Mathematics 2018-06-01 Léo Miolane

We consider signal source localization from range-difference measurements. First, we give some readily-checked conditions on measurement noises and sensor deployment to guarantee the asymptotic identifiability of the model and show the…

Signal Processing · Electrical Eng. & Systems 2023-09-26 Guangyang Zeng , Biqiang Mu , Ling Shi , Jiming Chen , Junfeng Wu