  A generalized additive model (GAM, Hastie and Tibshirani (1987)) is a
nonparametric model by the sum of univariate functions with respect to each
explanatory variable, i.e., $f({\mathbf x}) = \sum f_j(x_j)$, where
$x_j\in\mathbb{R}$ is $j$-th component of a sample ${\mathbf x}\in
\mathbb{R}^p$. In this paper, we introduce the total variation (TV) of a
function as a measure of the complexity of functions in $L^1_{\rm
c}(\mathbb{R})$-space. Our analysis shows that a GAM based on TV-regularization
exhibits a Rademacher complexity of $O(\sqrt{\frac{\log p}{m}})$, which is
tight in terms of both $m$ and $p$ in the agnostic case of the classification
problem. In result, we obtain generalization error bounds for finite samples
according to work by Bartlett and Mandelson (2002).
