New analysis of random projections optimizes spectral algorithms in Sobolev norms

This paper introduces an improved analysis of random projection-based spectral algorithms, focusing on their generalization performance under general conditions. The authors establish optimal learning rates in Sobolev norms, matching minimax lower bounds, by leveraging the embedding property of reproducing kernel Hilbert spaces. Their findings indicate that the projection dimension required for optimality is proportional to the effective dimension, significantly reducing computational costs while maintaining statistical efficiency across various source conditions. Experimental results validate the theoretical findings and practical effectiveness of the proposed method. AI

IMPACT Optimizes computational costs for spectral algorithms, potentially enabling more efficient data analysis in machine learning applications.

RANK_REASON The item is an academic paper detailing theoretical advancements in machine learning algorithms. [lever_c_demoted from research: ic=1 ai=1.0]

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