Denise: Deep Robust Principal Component Analysis for Positive Semidefinite Matrices

Calypso Herrera, Florian Krach, Anastasis Kratsios, Pierre Ruyssen and Josef Teichmann

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Abstract: The robust PCA of covariance matrices plays an essential role when isolating key explanatory features. The currently available methods for performing such a low-rank plus sparse decomposition are matrix specific, meaning, those algorithms must re-run for every new matrix. Since these algorithms are computationally expensive, it is preferable to learn and store a function that nearly instantaneously performs this decomposition when evaluated. Therefore, we introduce Denise, a deep learning-based algorithm for robust PCA of covariance matrices, or more generally, of symmetric positive semidefinite matrices, which learns precisely such a function. Theoretical guarantees for Denise are provided. These include a novel universal approximation theorem adapted to our geometric deep learning problem and convergence to an optimal solution to the learning problem. Our experiments show that Denise matches state-of-the-art performance in terms of decomposition quality, while being approximately $2000\times$ faster than the state-of-the-art, principal component pursuit (PCP), and $200 \times$ faster than the current speed-optimized method, fast PCP.

Date: 2020-04, Revised 2023-06
New Economics Papers: this item is included in nep-big and nep-cmp
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Published in Transactions on Machine Learning Research (2023)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2004.13612

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