  We obtain a tight distribution-specific characterization of the sample
complexity of large-margin classification with L_2 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
\gamma-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.
