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In 1-bit compressive sensing, each measurement is quantized to a single bit, namely the sign of a linear function of an unknown vector, and the goal is to accurately recover the vector. While it is most popular to assume a standard Gaussian…

Machine Learning · Computer Science 2021-08-10 Zhaoqiang Liu , Subhroshekhar Ghosh , Jun Han , Jonathan Scarlett

Unlike compressive sensing where the measurement outputs are assumed to be real-valued and have infinite precision, in "one-bit compressive sensing", measurements are quantized to one bit, their signs. In this work, we show how to recover…

Information Theory · Computer Science 2017-05-03 Jayadev Acharya , Arnab Bhattacharyya , Pritish Kamath

We consider unreliable distributed learning systems wherein the training data is kept confidential by external workers, and the learner has to interact closely with those workers to train a model. In particular, we assume that there exists…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-05-10 Lili Su , Jiaming Xu

Let $x\in\mathbb{C}^n$ be a spectrally sparse signal consisting of $r$ complex sinusoids with or without damping. We consider the spectral compressed sensing problem, which is about reconstructing $x$ from its partial revealed entries. By…

Optimization and Control · Mathematics 2017-08-01 Jian-Feng Cai , Tianming Wang , Ke Wei

Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…

Statistical Mechanics · Physics 2012-08-20 Florent Krzakala , Marc Mézard , François Sausset , Yifan Sun , Lenka Zdeborová

This letter investigates the joint recovery of a frequency-sparse signal ensemble sharing a common frequency-sparse component from the collection of their compressed measurements. Unlike conventional arts in compressed sensing, the…

Information Theory · Computer Science 2015-06-22 Zhenqi Lu , Rendong Ying , Sumxin Jiang , Peilin Liu , Wenxian Yu

In this work, we present a family of vector quantization schemes \emph{vqSGD} (Vector-Quantized Stochastic Gradient Descent) that provide an asymptotic reduction in the communication cost with convergence guarantees in first-order…

Machine Learning · Computer Science 2020-12-29 Venkata Gandikota , Daniel Kane , Raj Kumar Maity , Arya Mazumdar

Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…

Machine Learning · Statistics 2012-07-26 Alekh Agarwal , Sahand N. Negahban , Martin J. Wainwright

Distributed stochastic gradient descent (SGD) with gradient compression has become a popular communication-efficient solution for accelerating distributed learning. One commonly used method for gradient compression is Top-K sparsification,…

Machine Learning · Computer Science 2023-09-12 Mengzhe Ruan , Guangfeng Yan , Yuanzhang Xiao , Linqi Song , Weitao Xu

The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model targets a solution that has the least l0-norm among all signals…

Information Theory · Computer Science 2013-02-07 Lixin Shen , Bruce W. Suter

We consider the problem of recovering off-the-grid spikes from linear measurements. The state of the art Over-Parametrized Continuous Orthogonal Matching Pursuit (OP-COMP) with Projected Gradient Descent (PGD) successfully recovers those…

Numerical Analysis · Mathematics 2024-02-20 Pierre-Jean Bénard , Yann Traonmilin , Jean François Aujol

We study the problem of finding the best linear model that can minimize least-squares loss given a data-set. While this problem is trivial in the low dimensional regime, it becomes more interesting in high dimensions where the population…

Machine Learning · Computer Science 2021-02-09 Yahya Sattar , Samet Oymak

We consider the problem of decentralized consensus optimization, where the sum of $n$ smooth and strongly convex functions are minimized over $n$ distributed agents that form a connected network. In particular, we consider the case that the…

Machine Learning · Computer Science 2019-10-02 Amirhossein Reisizadeh , Aryan Mokhtari , Hamed Hassani , Ramtin Pedarsani

This paper investigates the recovery of a spectrally sparse signal from its partially revealed noisy entries within the framework of spectral compressive sensing. Nonconvex optimization approaches have recently been proposed based on…

Information Theory · Computer Science 2022-01-25 Xunmeng Wu , Zai Yang , Zongben Xu

We show that the gradient descent algorithm provides an implicit regularization effect in the learning of over-parameterized matrix factorization models and one-hidden-layer neural networks with quadratic activations. Concretely, we show…

Machine Learning · Computer Science 2019-02-15 Yuanzhi Li , Tengyu Ma , Hongyang Zhang

Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…

Information Theory · Computer Science 2009-11-26 Ali Hormati , Amin Karbasi , Soheil Mohajer , Martin Vetterli

We study the robust one-bit compressed sensing problem whose goal is to design an algorithm that faithfully recovers any sparse target vector $\theta_0\in\mathbb{R}^d$ \textit{uniformly} via $m$ quantized noisy measurements. Specifically,…

Statistics Theory · Mathematics 2020-08-25 Shuang Qiu , Xiaohan Wei , Zhuoran Yang

We study the problem of approximately recovering signals on a manifold from one-bit linear measurements drawn from either a Gaussian ensemble, partial circulant ensemble, or bounded orthonormal ensemble and quantized using Sigma-Delta or…

Information Theory · Computer Science 2019-04-25 Mark Iwen , Eric Lybrand , Aaron Nelson , Rayan Saab

In this paper, utilizing techniques in compressed sensing, parallel optimization and deep learning, we propose a model-driven approach to jointly design the common measurement matrix and GROUP LASSO-based jointly sparse signal recovery…

Information Theory · Computer Science 2020-02-10 Shuaichao Li , Wanqing Zhang , Ying Cui

The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…

Optimization and Control · Mathematics 2025-06-18 Lucka Barbeau , Marc-Étienne Lamarche-Gagnon , Florin Ilinca