\title{Covering Number Bounds of Certain Regularized Linear Function Classes}

\author{\name Tong Zhang  \email tzhang@watson.ibm.com \\
  \addr   T.J. Watson Research Center  \\
  Route 134, Yorktown Heights, NY 10598, U.S.A. \\
}

\editor{Peter L. Bartlett}

\date{}

\maketitle

\begin{abstract}
  Recently, sample complexity bounds have been derived for problems involving 
  linear functions such as neural networks and support vector machines.
  In many of  these theoretical studies, the concept of covering numbers 
  played an important role. It is thus useful to study covering numbers
  for linear function classes.
  In this paper, we investigate two closely related methods to derive upper 
  bounds on these  covering numbers. 
  The first method, already employed
  in some earlier studies, relies on the so-called Maurey's lemma; 
  the second method uses
  techniques from the  mistake bound framework in online learning.
  We compare results from these two methods, as well as their consequences in
  some learning formulations.
\end{abstract}