Robust distributed multicategory angle-based classification for massive data

Multicategory classification problems are frequently encountered in practice. Considering that the massive data sets are increasingly common and often stored locally, we first provide a distributed estimation in the multicategory angle-based classification framework and obtain its excess risk under general conditions. Further, under varied robustness settings, we develop two robust distributed algorithms to provide robust estimations of the multicategory classification. The first robust distributed algorithm takes advantage of median-of-means (MOM) and is designed by the MOM-based gradient estimation. The second robust distributed algorithm is implemented by constructing the weighted-based gradient estimation. The theoretical guarantees of our algorithms are established via the non-asymptotic error bounds of the iterative estimations. Some numerical simulations demonstrate that our methods can effectively reduce the impact of outliers.