Finite Sample Guarantees for PCA in Non-Isotropic and Data-Dependent Noise
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| Authors | Namrata Vaswani, Praneeth Narayanamurthy |
| Journal/Conference Name | 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017 |
| Paper Category | Artificial Intelligence |
| Paper Abstract | This work obtains novel finite sample guarantees for Principal Component Analysis (PCA). These hold even when the corrupting noise is non-isotropic, and a part (or all of it) is data-dependent. Because of the latter, in general, the noise and the true data are correlated. The results in this work are a significant improvement over those given in our earlier work where this "correlated-PCA" problem was first studied. In fact, in certain regimes, our results imply that the sample complexity required to achieve subspace recovery error that is a constant fraction of the noise level is near-optimal. Useful corollaries of our result include guarantees for PCA in sparse data-dependent noise and for PCA with missing data. An important application of the former is in proving correctness of the subspace update step of a popular online algorithm for dynamic robust PCA. |
| Date of publication | 2017 |
| Code Programming Language | Matlab |
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