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In this work we study convergence properties of sparse polynomial approximations for a class of affine parametric saddle point problems. Such problems can be found in many computational science and engineering fields, including the Stokes…

Numerical Analysis · Mathematics 2018-09-28 Peng Chen , Omar Ghattas

Greedy algorithms are popular in compressive sensing for their high computational efficiency. But the performance of current greedy algorithms can be degenerated seriously by noise (both multiplicative noise and additive noise). A robust…

Information Theory · Computer Science 2014-02-10 Yurrit Avonds , Yipeng Liu , Sabine Van Huffel

We study point processes that consist of certain centers of point tuples of an underlying Poisson process. Such processes arise in stochastic geometry in the study of exceedances of various functionals describing geometric properties of the…

Probability · Mathematics 2022-12-26 Moritz Otto

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…

Computation · Statistics 2018-03-15 Hongqiao Wang , Jinglai Li

The cosparse analysis model has been introduced recently as an interesting alternative to the standard sparse synthesis approach. A prominent question brought up by this new construction is the analysis pursuit problem -- the need to find a…

Functional Analysis · Mathematics 2014-01-06 Raja Giryes , Sangnam Nam , Michael Elad , Rémi Gribonval , Mike E. Davies

In the field of uncertainty quantification, sparse polynomial chaos (PC) expansions are commonly used by researchers for a variety of purposes, such as surrogate modeling. Ideas from compressed sensing may be employed to exploit this…

Methodology · Statistics 2018-05-09 Paul Diaz , Alireza Doostan , Jerrad Hampton

We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…

Statistics Theory · Mathematics 2012-02-24 Peter Hall , Tung Pham , M. P. Wand , S. S. J. Wang

The paper characterizes uniform convergence rate for general classes of wavelet expansions of stationary Gaussian random processes. The convergence in probability is considered.

Probability · Mathematics 2013-08-08 Andriy Olenko , Yuriy Kozachenko , Olga Polosmak

We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm…

Statistics Theory · Mathematics 2020-09-04 Benjamin Aubin , Bruno Loureiro , Antoine Baker , Florent Krzakala , Lenka Zdeborová

This paper studies the estimation of the conditional density f (x, $\times$) of Y i given X i = x, from the observation of an i.i.d. sample (X i , Y i) $\in$ R d , i = 1,. .. , n. We assume that f depends only on r unknown components with…

Statistics Theory · Mathematics 2021-06-29 Minh-Lien Jeanne Nguyen , Claire Lacour , Vincent Rivoirard

We give a general framework for approximations to combinatorial assemblies, especially suitable to the situation where the number $k$ of components is specified, in addition to the overall size $n$. This involves a Poisson process, which,…

Probability · Mathematics 2016-07-06 Richard Arratia , Stephen DeSalvo

In this paper, we study random subsampling of Gaussian process regression, one of the simplest approximation baselines, from a theoretical perspective. Although subsampling discards a large part of training data, we show provable guarantees…

Machine Learning · Statistics 2019-01-29 Kohei Hayashi , Masaaki Imaizumi , Yuichi Yoshida

Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-06-06 Sepehr Assadi , MohammadHossein Bateni , Vahab Mirrokni

Define the scaled empirical point process on an independent and identically distributed sequence $\{Y_i: i\le n\}$ as the random point measure with masses at $a_n^{-1} Y_i$. For suitable $a_n$ we obtain the weak limit of these point…

Probability · Mathematics 2016-08-16 André Dabrowski , Gail Ivanoof , Rafal Kulik

We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…

Statistics Theory · Mathematics 2009-09-29 Andrew R. Barron , Albert Cohen , Wolfgang Dahmen , Ronald A. DeVore

We study an inhomogeneous random connection model in the connectivity regime. The vertex set of the graph is a homogeneous Poisson point process $\mathcal{P}_s$ of intensity $s>0$ on the unit cube…

Probability · Mathematics 2021-06-23 Srikanth K. Iyer , Sanjoy Kr. Jhawar

We consider the issue of reporting the result of search experiment in the most unbiased and efficient way, i.e. in a way which allows an easy interpretation and combination of results and which do not depend on whether the experimenters…

High Energy Physics - Experiment · Physics 2007-05-23 P. Astone , G. D'Agostini

We provide a Poisson approximation result for dependent thinnings of Gibbs point processes as well as qualitative and quantitative central limit theorems for geometric functionals of Gibbs point processes in increasing observation windows.…

Probability · Mathematics 2026-01-27 Christian Hirsch , Moritz Otto , Anne Marie Svane

We prove a multidimensional Poisson limit theorem in free probability, and define joint free Poisson distributions in a non-commutative probability space. We define (compound) free Poisson process explicitly, similar to the definitions of…

Operator Algebras · Mathematics 2015-07-31 Guimei An , Mingchu Gao

We present an approximate Bayesian inference approach for estimating the intensity of an inhomogeneous Poisson process, where the intensity function is modelled using a Gaussian process (GP) prior via a sigmoid link function. Augmenting the…

Machine Learning · Statistics 2019-05-06 Christian Donner , Manfred Opper