Applied and Computational Harmonic Analysis最新文献_第5页

Mathematical foundation of sparsity-based multi-snapshot spectral estimation 基于稀疏性的多快照频谱估计的数学基础

IF 2.5 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-06-07 DOI: 10.1016/j.acha.2024.101673

Ping Liu , Sanghyeon Yu , Ola Sabet , Lucas Pelkmans , Habib Ammari

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引用次数: 0

Adaptive parameter selection for kernel ridge regression 核岭回归的自适应参数选择

IF 2.5 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-06-07 DOI: 10.1016/j.acha.2024.101671

Shao-Bo Lin

引用次数: 0

On the existence and estimates of nested spherical designs 关于嵌套球形设计的存在和估计

IF 2.5 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-06-04 DOI: 10.1016/j.acha.2024.101672

Ruigang Zheng, Xiaosheng Zhuang

引用次数: 0

A sharp sufficient condition for mobile sampling in terms of surface density 从表面密度看移动采样的充分条件

IF 2.5 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-05-23 DOI: 10.1016/j.acha.2024.101670

Benjamin Jaye , Mishko Mitkovski , Manasa N. Vempati

引用次数: 0

Towards a bilipschitz invariant theory 迈向双唇不变量理论

IF 2.5 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-05-14 DOI: 10.1016/j.acha.2024.101669

Jameson Cahill , Joseph W. Iverson , Dustin G. Mixon

引用次数: 0

Gaussian random field approximation via Stein's method with applications to wide random neural networks 通过斯坦因方法进行高斯随机场逼近并应用于宽随机神经网络

IF 2.5 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-05-13 DOI: 10.1016/j.acha.2024.101668

Krishnakumar Balasubramanian , Larry Goldstein , Nathan Ross , Adil Salim

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引用次数: 0

Differentially private federated learning with Laplacian smoothing 利用拉普拉斯平滑法进行差异化私有联合学习

IF 2.5 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-05-07 DOI: 10.1016/j.acha.2024.101660

Zhicong Liang , Bao Wang , Quanquan Gu , Stanley Osher , Yuan Yao

{"title":"Differentially private federated learning with Laplacian smoothing","authors":"Zhicong Liang , Bao Wang , Quanquan Gu , Stanley Osher , Yuan Yao","doi":"10.1016/j.acha.2024.101660","DOIUrl":"https://doi.org/10.1016/j.acha.2024.101660","url":null,"abstract":"<div><p>Federated learning aims to protect data privacy by collaboratively learning a model without sharing private data among users. However, an adversary may still be able to infer the private training data by attacking the released model. Differential privacy provides a statistical protection against such attacks at the price of significantly degrading the accuracy or utility of the trained models. In this paper, we investigate a utility enhancement scheme based on Laplacian smoothing for differentially private federated learning (DP-Fed-LS), to improve the statistical precision of parameter aggregation with injected Gaussian noise without losing privacy budget. Our key observation is that the aggregated gradients in federated learning often enjoy a type of smoothness, <em>i.e.</em> sparsity in a graph Fourier basis with polynomial decays of Fourier coefficients as frequency grows, which can be exploited by the Laplacian smoothing efficiently. Under a prescribed differential privacy budget, convergence error bounds with tight rates are provided for DP-Fed-LS with uniform subsampling of heterogeneous <strong>non-iid</strong> data, revealing possible utility improvement of Laplacian smoothing in effective dimensionality and variance reduction, among others. Experiments over MNIST, SVHN, and Shakespeare datasets show that the proposed method can improve model accuracy with DP-guarantee and membership privacy under both uniform and Poisson subsampling mechanisms.</p></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"72 ","pages":"Article 101660"},"PeriodicalIF":2.5,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140906086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The mystery of Carleson frames 卡莱森框架之谜

IF 2.5 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-04-17 DOI: 10.1016/j.acha.2024.101659

Ole Christensen , Marzieh Hasannasab , Friedrich M. Philipp , Diana Stoeva

引用次数: 0

Effectiveness of the tail-atomic norm in gridless spectrum estimation 无网格频谱估计中尾原子规范的有效性

IF 2.5 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2024-04-16 DOI: 10.1016/j.acha.2024.101658

Wei Li , Shidong Li , Jun Xian

引用次数: 0

Complex-order scale-invariant operators and self-similar processes 复阶尺度不变算子和自相似过程