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Related papers: AdaOja: Adaptive Learning Rates for Streaming PCA

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Oja's rule [Oja, Journal of mathematical biology 1982] is a well-known biologically-plausible algorithm using a Hebbian-type synaptic update rule to solve streaming principal component analysis (PCA). Computational neuroscientists have…

Neurons and Cognition · Quantitative Biology 2020-06-19 Chi-Ning Chou , Mien Brabeeba Wang

This work provides improved guarantees for streaming principle component analysis (PCA). Given $A_1, \ldots, A_n\in \mathbb{R}^{d\times d}$ sampled independently from distributions satisfying $\mathbb{E}[A_i] = \Sigma$ for $\Sigma \succeq…

Machine Learning · Computer Science 2016-03-29 Prateek Jain , Chi Jin , Sham M. Kakade , Praneeth Netrapalli , Aaron Sidford

Since its inception in 1982, Oja's algorithm has become an established method for streaming principle component analysis (PCA). We study the problem of streaming PCA, where the data-points are sampled from an irreducible, aperiodic, and…

Statistics Theory · Mathematics 2023-06-21 Syamantak Kumar , Purnamrita Sarkar

Oja's algorithm for Streaming Principal Component Analysis (PCA) for $n$ data-points in a $d$ dimensional space achieves the same sin-squared error $O(r_{\mathsf{eff}}/n)$ as the offline algorithm in $O(d)$ space and $O(nd)$ time and a…

Statistics Theory · Mathematics 2025-03-12 Syamantak Kumar , Purnamrita Sarkar

Principal Component Analysis (PCA) is a widely used technique in machine learning, data analysis and signal processing. With the increase in the size and complexity of datasets, it has become important to develop low-space usage algorithms…

Machine Learning · Computer Science 2023-03-09 Yichuan Deng , Zhao Song , Zifan Wang , Han Zhang

In this paper we propose a new algorithm for streaming principal component analysis. With limited memory, small devices cannot store all the samples in the high-dimensional regime. Streaming principal component analysis aims to find the…

Machine Learning · Statistics 2018-02-16 Puyudi Yang , Cho-Jui Hsieh , Jane-Ling Wang

Low-precision streaming PCA estimates the top principal component in a streaming setting under limited precision. We establish an information-theoretic lower bound on the quantization resolution required to achieve a target accuracy for the…

Machine Learning · Computer Science 2025-10-28 Sanjoy Dasgupta , Syamantak Kumar , Shourya Pandey , Purnamrita Sarkar

We analyze Oja's algorithm for streaming $k$-PCA and prove that it achieves performance nearly matching that of an optimal offline algorithm. Given access to a sequence of i.i.d. $d \times d$ symmetric matrices, we show that Oja's algorithm…

Data Structures and Algorithms · Computer Science 2021-02-09 De Huang , Jonathan Niles-Weed , Rachel Ward

Fair Principal Component Analysis (PCA) is a problem setting where we aim to perform PCA while making the resulting representation fair in that the projected distributions, conditional on the sensitive attributes, match one another.…

Machine Learning · Statistics 2023-10-31 Junghyun Lee , Hanseul Cho , Se-Young Yun , Chulhee Yun

We study streaming principal component analysis (PCA), that is to find, in $O(dk)$ space, the top $k$ eigenvectors of a $d\times d$ hidden matrix $\bf \Sigma$ with online vectors drawn from covariance matrix $\bf \Sigma$. We provide…

Optimization and Control · Mathematics 2017-04-18 Zeyuan Allen-Zhu , Yuanzhi Li

In this paper we analyze the behavior of the Oja's algorithm for online/streaming principal component subspace estimation. It is proved that with high probability it performs an efficient, gap-free, global convergence rate to approximate an…

Machine Learning · Computer Science 2024-03-06 Xin Liang

Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/\Delta)$ full-data passes to recover the principal component of a matrix with…

Optimization and Control · Mathematics 2017-07-11 Christopher De Sa , Bryan He , Ioannis Mitliagkas , Christopher Ré , Peng Xu

We propose a novel statistical inference framework for streaming principal component analysis (PCA) using Oja's algorithm, enabling the construction of confidence intervals for individual entries of the estimated eigenvector. Most existing…

Statistics Theory · Mathematics 2025-07-22 Syamantak Kumar , Shourya Pandey , Purnamrita Sarkar

In this paper, we propose to adopt the diffusion approximation tools to study the dynamics of Oja's iteration which is an online stochastic gradient descent method for the principal component analysis. Oja's iteration maintains a running…

Machine Learning · Statistics 2018-08-30 Chris Junchi Li , Mengdi Wang , Han Liu , Tong Zhang

This paper studies the complexity of the stochastic gradient algorithm for PCA when the data are observed in a streaming setting. We also propose an online approach for selecting the learning rate. Simulation experiments confirm the…

Statistics Theory · Mathematics 2018-04-04 Stephane Chretien , Christophe Guyeux , Zhen-Wai Olivier HO

We study the problem of recovering the subspace spanned by the first $k$ principal components of $d$-dimensional data under the streaming setting, with a memory bound of $O(kd)$. Two families of algorithms are known for this problem. The…

Machine Learning · Statistics 2015-10-13 Chun-Liang Li , Hsuan-Tien Lin , Chi-Jen Lu

Learning for maximizing AUC performance is an important research problem in Machine Learning and Artificial Intelligence. Unlike traditional batch learning methods for maximizing AUC which often suffer from poor scalability, recent years…

Machine Learning · Computer Science 2016-02-02 Yi Ding , Peilin Zhao , Steven C. H. Hoi , Yew-Soon Ong

Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…

Computation · Statistics 2018-11-06 Victor Minden , Cengiz Pehlevan , Dmitri B. Chklovskii

We consider streaming principal component analysis when the stochastic data-generating model is subject to perturbations. While existing models assume a fixed covariance, we adopt a robust perspective where the covariance matrix belongs to…

Machine Learning · Statistics 2022-10-13 Daniel Bienstock , Minchan Jeong , Apurv Shukla , Se-Young Yun

We consider streaming, one-pass principal component analysis (PCA), in the high-dimensional regime, with limited memory. Here, $p$-dimensional samples are presented sequentially, and the goal is to produce the $k$-dimensional subspace that…

Machine Learning · Statistics 2013-07-02 Ioannis Mitliagkas , Constantine Caramanis , Prateek Jain
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