We introduce Denise, a deep learning based algorithm for decomposing positive semidefinite matrices into the sum of a low rank plus a sparse matrix. The deep neural network is trained on a randomly generated dataset using the Cholesky factorization. This method, benchmarked on synthetic datasets as well as on some S P500 stock returns covariance matrices ,  achieves comparable results to several state-of-the-art techniques, while outperforming all existing algorithms in terms of computational time. Finally, theoretical results concerning the convergence of the training are derived .
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 matrix should 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 .
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We
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 matrix should 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
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learning based algorithm for decomposing
learning-based algorithm for robust PCA of symmetric
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into the sum of a low rank plus a sparse matrix. The deep neural network is trained
, 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
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using the Cholesky factorization. This method, benchmarked on synthetic datasets as well as on some S
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P500 stock returns covariance matrices
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and evaluate the performance of the DNN on synthetic and real-world covariance matrices. Denise
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techniques, while outperforming
algorithms in terms of decomposition quality, but as only one evaluation of the learned DNN is needed, Denise outperforms
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computational time. Finally, theoretical results concerning the convergence of the training are derived
computation time