Group Sparse Additive Machine
A family of learning algorithms generated from additive models have attracted much attention recently for their flexibility and interpretability in high dimensional data analysis. Among them, learning models with grouped variables have shown competitive performance for prediction and variable selection. However, the previous works mainly focus on the least squares regression problem, not the classification task. Thus, it is desired to design the new additive classification model with variable selection capability for many real-world applications which focus on high-dimensional data classification. To address this challenging problem, in this paper, we investigate the classification with group sparse additive models in reproducing kernel Hilbert spaces. A novel classification method, called as group sparse additive machine (GroupSAM), is proposed to explore and utilize the structure information among the input variables. Generalization error bound is derived and proved by integrating the sample error analysis with empirical covering numbers and the hypothesis error estimate with the stepping stone technique. Our new bound shows that GroupSAM can achieve a satisfactory learning rate with polynomial decay. Experimental results on synthetic data and seven benchmark datasets consistently show the effectiveness of our new approach.
This paper presents a new additive classification model (GroupSAM) with grouped variables based on group based additive models in kernel Hilbert spaces, and an upper bound for the generalization error is provided in Theorem 1 to show that GroupSAM converges to the optimal error with a polynomial decay under certain conditions. Experiments are performed on synthetic data and seven UCI datasets that have been modified in order to get some group structure in the feature space. The results provided in the paper show that the proposed method is able to take into account grouped features while yielding good performance in terms of classification accuracy.
As far as I know, the paper presents a novel method for group sparse nonlinear classification with additive models. However, the degree of contribution of this paper with respect to 
Yin, Junming, Xi Chen, and Eric P. Xing. "Group sparse additive models." Proceedings of the... International Conference on Machine Learning. International Conference on Machine Learning. Vol. 2012. NIH Public Access, 2012.
Is not clear to me as the framework presented in the above paper seems to be easy to extend to classification settings. In fact, Yin et al. apply their group sparse additive model for regression to address a classification task (classification of breast cancer data) by taking the sign of the predicted responses. On the other hand, I appreciate authors’ efforts in providing a theoretical analysis on the generalization error bound of GroupSAM and tis convergence.
Regarding the empirical results, I do not think that the experiments show the real significance of the proposed method as they real-world data has been “arbitrarily” tuned to enforce group structure. I think that the use of real data with group structure by itself is mandatory in order to properly measure the contribution of this work. For example, in bioinformatics in can be useful to build predictive models that take into account genes’ pathway information.  I also miss comparisons with other parametric approaches such as Group Lasso or the GroupSpSAM model adapted to the classification setting. Additionally, I cannot see a clear advantage with respect to Gaussian SVMs in terms of classification accuracy. I also would like to know whether the Gaussian kernel parameter was properly tuned.
Finally, I would like to know how multiclass classification was performed in the toy example as the GroupSAM method is formulated in Section 2 for binary classification problems. 
Overall, the paper is well written and it has a well structure. However, I think that the introduction does not clearly present the differences between the proposed approach and other sparse additive models and group sparse models in parametric settings (e.g. Group Lasso).