## Statistical Learnability of Generalized Additive Models based on Total Variation Regularization

8 Feb 2018  ·  ·

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). read more

PDF Abstract

# Code Add Remove Mark official

No code implementations yet. Submit your code now

# Datasets

Add Datasets introduced or used in this paper

# Results from the Paper Add Remove

Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.