Tight Sample Complexity of Large-Margin Learning
Sivan Sabato, Nathan Srebro and Naftali Tishby
In: NIPS 2010, 6-9 Dec 2010, Vancouver, Canada.
We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the gamma-adapted-dimension, which is a simple function of the spectrum of a distribution’s
covariance matrix, and show distribution-specific upper and lower bounds on the sample complexity, both governed by the
-adapted-dimension of the source distribution. We conclude that this new quantity tightly characterizes the true sample complexity of large-margin classification. The bounds hold for a rich family of sub-Gaussian distributions.