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arXiv Machine Learning By Caixing Wang, Yue Wang

Random Projections for Spectral Algorithms: Optimal Rates in Sobolev Norms

Read the original on arXiv Machine Learning →

The paper studies random projections (RP) for spectral algorithms, providing a comprehensive analysis of their generalization performance under broad conditions. By exploiting the RKHS embedding property and operator similarity, it establishes optimal learning rates in Sobolev norms that match minimax lower bounds up to logarithmic factors. For common RP implementations—randomized sketches and Nyström sub-sampling—the required projection dimension scales with the effective dimension, reducing computational cost while preserving statistical efficiency.

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