The robust PCA of high-dimensional 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, the algorithm must re-run each time a new matrixshould be decomposed . Since these algorithms are computationally expensive, it is preferable to learn and store a function that instantaneously performs this decomposition when evaluated. Therefore, we introduce Denise, a deep learning-based algorithm for robust PCA of  symmetric positive semidefinite matrices, which learns precisely such a function. Theoretical guarantees that Denise 's architecture can approximate the decomposition function, to arbitrary precision and with arbitrarily high probability, are obtained. The training scheme is also shown to convergence to a stationary point of the robust PCA's loss-function. We train Denise on a randomly generated dataset, and evaluate the performance of the DNN on synthetic and real-world covariance matrices. Denise achieves comparable results to several state-of-the-art algorithms in terms of decomposition quality, but as only one evaluation of the learned DNN is needed, Denise outperforms all existing algorithms in terms of computation time .
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 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, convergence to an optimal solution of the learning problem and convergence of the training scheme. Our experiments show that Denise matches state-of-the-art performance in terms of decomposition quality, while being approximately 2000x faster than the state-of-the-art, PCP, and 200x faster than the current speed optimized method, fast PCP .
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high-dimensional
covariance
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the algorithm
those algorithms
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each time a new matrixshould be decomposed
for every new matrix
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covariance matrices, or more generally of
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that Denise 's architecture can approximate the decomposition function, to arbitrary precision and with arbitrarily high probability, are obtained. The training scheme is also shown to convergence to a stationary point of the robust PCA's loss-function. We train Denise on a randomly generated dataset, and evaluate the performance of the DNN on synthetic and real-world covariance matrices. Denise achieves comparable results to several
for Denise are provided. These include a novel universal approximation theorem adapted to our geometric deep learning problem, convergence to an optimal solution of the learning problem and convergence of the training scheme. Our experiments show that Denise matches
R
algorithms
performance
R
but as only one evaluation of the learned DNN is needed, Denise outperforms all existing algorithms in terms of computation time
while being approximately 2000x faster than the state-of-the-art, PCP, and 200x faster than the current speed optimized method, fast PCP