Reproduce “Optimal Rates for Adaptive Private $k$-PCA” on OpenResearch
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About this paper
Johanna Düngler, Amartya Sanyal
The authors introduce AdaDPO, a private stochastic method for estimating the leading k-dimensional covariance subspace. It privately estimates projected-sample fluctuations around a center and updates all directions jointly. TAdaDPO refines a warm start through orthogonal updates. Under stated assumptions, AdaDPO has optimal dimension and k dependence; under flat-tail Gaussian conditions, TAdaDPO achieves a sharper spectral error rate, subject to warm-start and lower-order-term conditions.
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