Related papers: Optimality of Gradient-MUSIC for spectral estimati…
We develop a multidimensional version of Gradient-MUSIC for estimating the frequencies of a nonharmonic signal from noisy samples. The guiding principle is that frequency recovery should be based only on the signal subspace determined by…
This paper presents a performance analysis of the MUltiple SIgnal Classification (MUSIC) algorithm applied on $D$ dimensional single-snapshot spectral estimation while $s$ true frequencies are located on the continuum of a bounded domain.…
We propose an efficient algorithm for reconstructing one-dimensional wide-band line spectra from their Fourier data in a bounded interval $[-\Omega,\Omega]$. While traditional subspace methods such as MUSIC achieve super-resolution for…
The MUSIC algorithm, with its extension for imaging sparse {\em extended} objects, is analyzed by compressed sensing (CS) techniques. The notion of restricted isometry property (RIP) and an upper bound on the restricted isometry constant…
This paper studies the problem of line spectral estimation in the continuum of a bounded interval with one snapshot of array measurement. The single-snapshot measurement data is turned into a Hankel data matrix which admits the Vandermonde…
Gradient-type distributed optimization methods have blossomed into one of the most important tools for solving a minimization learning task over a networked agent system. However, only one gradient update per iteration is difficult to…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
The high computational complexity of the multiple signal classification (MUSIC) algorithm is mainly caused by the subspace decomposition and spectrum search, especially for frequent real-time applications or massive sensors. In this paper,…
Stochastic gradient descent (SGD) is one of the most popular algorithms in modern machine learning. The noise encountered in these applications is different from that in many theoretical analyses of stochastic gradient algorithms. In this…
Studying the properties of stochastic noise to optimize complex non-convex functions has been an active area of research in the field of machine learning. Prior work has shown that the noise of stochastic gradient descent improves…
The graduated optimization approach is a method for finding global optimal solutions for nonconvex functions by using a function smoothing operation with stochastic noise. This paper makes three contributions regarding graduated…
Decentralized optimization is typically studied under the assumption of noise-free transmission. However, real-world scenarios often involve the presence of noise due to factors such as additive white Gaussian noise channels or…
We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…
In this work, we describe a generic approach to show convergence with high probability for both stochastic convex and non-convex optimization with sub-Gaussian noise. In previous works for convex optimization, either the convergence is only…
Recently, the study of heavy-tailed noises in first-order nonconvex stochastic optimization has gotten a lot of attention since it was recognized as a more realistic condition as suggested by many empirical observations. Specifically, the…
This article deals with the problem of the statistical performance analysis of the MUSIC ( Multiple Signal Classification ) algorithm which is an eigen decomposition based method for the estimation of the angles of arrival of signals…
It has been observed in a variety of contexts that gradient descent methods have great success in solving low-rank matrix factorization problems, despite the relevant problem formulation being non-convex. We tackle a particular instance of…
One of the classical approaches for estimating the frequencies and damping factors in a spectrally sparse signal is the MUSIC algorithm, which exploits the low-rank structure of an autocorrelation matrix. Low-rank matrices have also…
We introduce a general framework for nonlinear stochastic gradient descent (SGD) for the scenarios when gradient noise exhibits heavy tails. The proposed framework subsumes several popular nonlinearity choices, like clipped, normalized,…
We introduce a detailed analysis of the convergence of first-order methods with composite noise (sum of relative and absolute) in gradient for convex and smooth function minimization. This paper illustrates instances of practical problems…