The paper derives sharp matching convergence rates for spectral methods in linear regression via feature space decomposition, enabling pre-ordering of algorithms and generalizing saturation effects.
Lepskii Principle in Supervised Learning
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abstract
In the setting of supervised learning using reproducing kernel methods, we propose a data-dependent regularization parameter selection rule that is adaptive to the unknown regularity of the target function and is optimal both for the least-square (prediction) error and for the reproducing kernel Hilbert space (reconstruction) norm error. It is based on a modified Lepskii balancing principle using a varying family of norms.
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Sharp convergence rates for Spectral methods via the feature space decomposition method
The paper derives sharp matching convergence rates for spectral methods in linear regression via feature space decomposition, enabling pre-ordering of algorithms and generalizing saturation effects.