# Streaming k-PCA: Efficient guarantees for Oja's algorithm, beyond rank-one updates

@inproceedings{Huang2021StreamingKE, title={Streaming k-PCA: Efficient guarantees for Oja's algorithm, beyond rank-one updates}, author={De Huang and Jonathan Niles-Weed and Rachel A. Ward}, booktitle={Annual Conference Computational Learning Theory}, year={2021} }

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× d symmetric matrices, we show that Oja’s algorithm can obtain an accurate approximation to the subspace of the top k eigenvectors of their expectation using a number of samples that scales polylogarithmically with d. Previously, such a result was only known in the case where the updates have rank one. Our analysis is…

## 7 Citations

### On the equivalence of Oja's algorithm and GROUSE

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It is shown that the Grassmannian Rank-One Subspace Estimation (GROUSE) algorithm is indeed equivalent to Oja’s algorithm in the sense that, at each iteration, given a step size for one of the algorithms, it may construct a step sizes for the other algorithm that results in an identical update.

### On the Optimality of the Oja's Algorithm for Online PCA

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It is proved that with high probability Oja’s algorithm performs an efficient, gap-free, global convergence rate to approximate an principal component subspace for any sub-Gaussian distribution.

### Bootstrapping the Error of Oja's Algorithm

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A stochastic Gauss-Newton (SGN) algorithm to study the online principal component analysis (OPCA) problem, which is formulated by using the symmetric low-rank product model for dominant eigenspace calculation, is proposed.

### Robust Streaming PCA

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- 2019

This work considers streaming principal component analysis when the stochastic data-generating model is subject to perturbations and provides fundamental limits on convergence of any algorithm recovering principal components.

### Preference Dynamics Under Personalized Recommendations

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This work shows how to design a content recommendations which can achieve approximate stationarity, under mild conditions on the set of available content, when a user's preferences are known, and how one can learn enough about a users' preferences to implement such a strategy even when user preferences are initially unknown.

### On the Correspondence between Gaussian Processes and Geometric Harmonics

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The correspondence between Gaussian process regression and Geometric Harmonics is discussed, providing alternative interpretations of uncertainty in terms of error estimation, or leading towards accelerated Bayesian Optimization due to dimensionality reduction.

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