论文信息 - A closer look at covering number bounds for Gaussian kernels

A closer look at covering number bounds for Gaussian kernels

We establish some new bounds on the log-covering numbers of (anisotropic) Gaussian reproducing kernel Hilbert spaces. Unlike previous results in this direction we focus on small explicit constants and their dependency on crucial parameters such as the kernel bandwidth and the size and dimension of the underlying space.

Ingo Steinwart | Simon Fischer

[1] Andreas Christmann,et al. Support vector machines , 2008, Data Mining and Knowledge Discovery Handbook.

[2] A. Kolmogorov,et al. Entropy and "-capacity of sets in func-tional spaces , 1961 .

[3] Ding-Xuan Zhou,et al. Capacity of reproducing kernel spaces in learning theory , 2003, IEEE Transactions on Information Theory.

[4] Van Der Vaart,et al. Adaptive Bayesian estimation using a Gaussian random field with inverse Gamma bandwidth , 2009, 0908.3556.

[5] S. Mahadevan,et al. Learning Theory , 2001 .

[6] Dino Sejdinovic,et al. Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences , 2018, ArXiv.

[7] Ingo Steinwart,et al. Learning rates for kernel-based expectile regression , 2018, Machine Learning.

[8] Carl E. Rasmussen,et al. Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[9] S. Smale,et al. ESTIMATING THE APPROXIMATION ERROR IN LEARNING THEORY , 2003 .

[10] Ingo Steinwart,et al. Optimal regression rates for SVMs using Gaussian kernels , 2013 .

[11] Thomas Kühn,et al. Covering numbers of Gaussian reproducing kernel Hilbert spaces , 2011, J. Complex..

[12] B. Carl,et al. Entropy, Compactness and the Approximation of Operators , 1990 .

[13] Ding-Xuan Zhou,et al. The covering number in learning theory , 2002, J. Complex..

[14] Bernhard Schölkopf,et al. Learning with kernels , 2001 .

[15] C. Tsallis. Entropy , 2022, Thermodynamic Weirdness.