Introduces alignment-sensitive effective span dimension (ESD) for learned-kernel spectral algorithms and proves minimax excess risk bounds of order sigma^2 * ESD, with gradient flow shown to reduce ESD.
By Grönwall inequality, we have |β(t)| ≤a 0 exp √ 2ebD 0 Z t T1 (|θ∗|+|ξ|)ds , t∈(T 1, T2)
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Alignment-Sensitive Minimax Rates for Spectral Algorithms with Learned Kernels
Introduces alignment-sensitive effective span dimension (ESD) for learned-kernel spectral algorithms and proves minimax excess risk bounds of order sigma^2 * ESD, with gradient flow shown to reduce ESD.