Simultaneous safe screening of features and samples in doubly sparse modeling

The problem of learning a sparse model is conceptually interpreted as the process of identify-ing active features/samples and then optimizing the model over them. Recently introduced safe screening allows us to identify a part of non- Active features/samples. So far, safe screening has been individually studied either for feature screening or for sample screening. In this paper, we introduce a new approach for safely screening features and samples simultaneously by al-ternatively iterating feature and sample screening steps. A significant advantage of considering them simultaneously rather than individually is that they have a synergy effect in the sense that the results of the previous safe feature screening can be exploited for improving the next safe sample screening performances, and vice- versa. We first theoretically investigate the synergy effect, and then illustrate the practical advantage through intensive numerical experiments for problems with large numbers of features and samples.