A randomized algorithm based on the basic SDP relaxation for sparse PCA achieves an approximation ratio bounded by the sparsity constant with high probability and O(log d) on average under a technical assumption satisfied for low-rank or exponentially decaying eigenvalue SDP solutions.
Exact and approximation algorithms for sparse pca
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Sp-GD recovers sparse max-affine parameters to epsilon accuracy with O(s log(d/s)) samples in the noise-free case under sub-Gaussian assumptions, supported by sparse-PCA initialization and an RMD transformation for generalized polynomials.
New MIP estimator for sparse PCA under spiked covariance model with statistical guarantees and custom solver scaling to 20,000 features.
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A Randomized Algorithm for Sparse PCA based on the Basic SDP Relaxation
A randomized algorithm based on the basic SDP relaxation for sparse PCA achieves an approximation ratio bounded by the sparsity constant with high probability and O(log d) on average under a technical assumption satisfied for low-rank or exponentially decaying eigenvalue SDP solutions.
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Sparse Max-Affine Regression
Sp-GD recovers sparse max-affine parameters to epsilon accuracy with O(s log(d/s)) samples in the noise-free case under sub-Gaussian assumptions, supported by sparse-PCA initialization and an RMD transformation for generalized polynomials.
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Sparse PCA: A New Scalable Estimator Based On Integer Programming
New MIP estimator for sparse PCA under spiked covariance model with statistical guarantees and custom solver scaling to 20,000 features.