Nonasymptotic Guarantees for Spiked Matrix Recovery with Generative Priors

Understand

Many problems in statistics and machine learning require the reconstruction of a rank-one signal matrix from noisy data.

• Enforcing additional prior information on the rank-one component is often key to guaranteeing good recovery performance.
• One such prior on the low-rank component is sparsity, giving rise to the sparse principal component analysis problem.
• Unfortunately, there is strong evidence that this problem suffers from a computational-to-statistical gap, which may be fundamental.