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Low rank approximation has been extensively studied in the past. It is most suitable to reproduce rectangular like structures in the data. In this work we introduce a generalization using shifted rank-1 matrices to approximate…

Numerical Analysis · Mathematics 2018-10-04 Florian Boßmann , Jianwei Ma

We consider the problem of optimal recovery of an element $u$ of a Hilbert space $\mathcal{H}$ from $m$ measurements obtained through known linear functionals on $\mathcal{H}$. Problems of this type are well studied \cite{MRW} under an…

Numerical Analysis · Mathematics 2015-06-17 Peter Binev , Albert Cohen , Wolfgang Dahmen , Ronald DeVore , Guergana Petrova , Przemyslaw Wojtaszczyk

The present paper concerns large covariance matrix estimation via composite minimization under the assumption of low rank plus sparse structure. In this approach, the low rank plus sparse decomposition of the covariance matrix is recovered…

Methodology · Statistics 2019-12-16 Matteo Farnè , Angela Montanari

This paper provides a unified treatment to the recovery of structured signals living in a star-shaped set from general quantized measurements $\mathcal{Q}(\mathbf{A}\mathbf{x}-\mathbf{\tau})$, where $\mathbf{A}$ is a sensing matrix,…

Information Theory · Computer Science 2025-04-29 Junren Chen , Ming Yuan

The problem of phase synchronization is to estimate the phases (angles) of a complex unit-modulus vector $z$ from their noisy pairwise relative measurements $C = zz^* + \sigma W$, where $W$ is a complex-valued Gaussian random matrix. The…

Optimization and Control · Mathematics 2018-04-10 Yiqiao Zhong , Nicolas Boumal

This study introduces a novel estimation method for the entries and structure of a matrix $A$ in the linear factor model $\mathbf{X} = A\textbf{Z} + \textbf{E}$. This is applied to an observable vector $\mathbf{X} \in \mathbb{R}^d$ with…

Statistics Theory · Mathematics 2024-10-18 Alexis Boulin

This paper deals with the estimation of the modes of an univariate mixture when the number of components is known and when the component density are well separated. We propose an algorithm based on the minimization of the "kp" criterion we…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Nicolas Paul , Luc Fety , Michel Terre

We define a notion of isotropy for discrete set distributions. If $\mu$ is a distribution over subsets $S$ of a ground set $[n]$, we say that $\mu$ is in isotropic position if $P[e \in S]$ is the same for all $e\in [n]$. We design a new…

Data Structures and Algorithms · Computer Science 2020-04-21 Nima Anari , Michał Dereziński

Spiking neural networks (SNNs), a brain-inspired computing paradigm, are emerging for their inference performance, particularly in terms of energy efficiency and latency attributed to the plasticity in signal processing. To deploy SNNs in…

Signal Processing · Electrical Eng. & Systems 2024-07-15 Sizhen Bian , Elisa Donati , Michele Magno

The general sequential decision-making problem, which includes Markov decision processes (MDPs) and partially observable MDPs (POMDPs) as special cases, aims at maximizing a cumulative reward by making a sequence of decisions based on a…

Machine Learning · Computer Science 2024-02-07 Ruiquan Huang , Yingbin Liang , Jing Yang

Compressed Sensing decoding algorithms can efficiently recover an N dimensional real-valued vector x to within a factor of its best k-term approximation by taking m = 2klog(N/k) measurements y = Phi x. If the sparsity or approximate…

Numerical Analysis · Mathematics 2008-12-09 Rachel Ward

We consider an inverse problem $\mathbf{y}= f(\mathbf{Ax})$, where $\mathbf{x}\in\mathbb{R}^n$ is the signal of interest, $\mathbf{A}$ is the sensing matrix, $f$ is a nonlinear function and $\mathbf{y} \in \mathbb{R}^m$ is the measurement…

Information Theory · Computer Science 2023-08-22 Junjie Ma , Ji Xu , Arian Maleki

We provide a rigorous random matrix theory analysis of spiked cross-covariance models where the signals across two high-dimensional data channels are partially aligned. These models are motivated by multi-modal learning and form the…

Statistics Theory · Mathematics 2026-02-23 Pierre Mergny , Lenka Zdeborová

Let $\hat\Sigma=\frac{1}{n}\sum_{i=1}^n X_i\otimes X_i$ denote the sample covariance operator of centered i.i.d.~observations $X_1,\dots,X_n$ in a real separable Hilbert space, and let $\Sigma=\mathbb{E}(X_1\otimes X_1)$. The focus of this…

Statistics Theory · Mathematics 2024-01-25 Miles E. Lopes

The mean squared displacement (MSD) of particles or probes is commonly estimated from microscopy videos using particle tracking approaches, which rely on tuning parameters manually, and are often unstable over the entire lag time range,…

Applications · Statistics 2026-05-29 Tong Lin , Jinseok Lee , Matt Helgeson , Megan T. Valentine , Yimin Luo , Mengyang Gu

A novel stochastic technique combining a dilute source grid of $\mathbb{Z}_3$ noise with iterative momentum-smearing is used to study the proton correlation function at rest and in boosted frames on two lattice volumes. The technique makes…

High Energy Physics - Lattice · Physics 2018-12-05 J. -J. Wu , W. Kamleh , D. ~B. Leinweber , R. D. Young , J. M. Zanotti

We study generative compressed sensing when the measurement matrix is randomly subsampled from a unitary matrix (with the DFT as an important special case). It was recently shown that $\textit{O}(kdn\| \boldsymbol{\alpha}\|_{\infty}^{2})$…

Information Theory · Computer Science 2023-11-21 Aaron Berk , Simone Brugiapaglia , Yaniv Plan , Matthew Scott , Xia Sheng , Ozgur Yilmaz

A class of robust estimators of scatter applied to information-plus-impulsive noise samples is studied, where the sample information matrix is assumed of low rank; this generalizes the study of (Couillet et al., 2013b) to spiked random…

Probability · Mathematics 2014-05-01 Romain Couillet

We revisit the classical problem of finding an approximately stationary point of the average of $n$ smooth and possibly nonconvex functions. The optimal complexity of stochastic first-order methods in terms of the number of gradient…

Machine Learning · Computer Science 2022-06-07 Alexander Tyurin , Lukang Sun , Konstantin Burlachenko , Peter Richtárik

We study the problem of partitioning a small sample of $n$ individuals from a mixture of $k$ product distributions over a Boolean cube $\{0, 1\}^K$ according to their distributions. Each distribution is described by a vector of allele…

Machine Learning · Computer Science 2008-02-21 Shuheng Zhou