Data-Driven Pinball-Loss Selection for Vertically Distributed Elastic-Net SVMs

2026-08-01

AI Summary

This work addresses the limitation of conventional pinball-loss support vector machines (SVMs), which require pre-specified asymmetric parameters that are often ill-suited to the intrinsic data characteristics. To overcome this, the authors propose a data-driven elastic-net SVM that adaptively selects an optimal loss function by learning simplex-constrained weights over a set of candidate pinball losses, thereby enabling data-dependent loss adaptation. A column-partitioned variable-splitting algorithm is further developed to facilitate scalable training in high-dimensional vertically partitioned distributed settings. Theoretical analysis guarantees that the proposed method achieves an objective value no worse than that of the best fixed-parameter configuration. Empirical results confirm its superior predictive performance and demonstrate numerical equivalence between centralized and distributed implementations, along with strong multi-process scalability.

Abstract

The pinball-loss support vector machine is robust, but its asymmetry parameter is usually fixed in advance. We propose a data-driven elastic-net support vector machine that learns simplex-constrained weights over candidate pinball losses while retaining one classifier. The weighted loss is equivalent to a pinball loss with a data-dependent effective parameter. An empirical oracle inequality shows that, when weight regularization and simplex truncation vanish, the classifier objective at a global minimizer does not exceed that of the best fixed candidate; otherwise, the excess is explicitly bounded. For high-dimensional data, we develop a column-partitioned variable-splitting solver. It converges with a best-iterate $O(1/T)$ squared-step residual rate. Under common initialization and global parameters, any column partition produces, in exact arithmetic, the same iterates and solution as centralized training. Experiments assess predictive behavior, numerical equivalence, and multi-process scalability.

Problem

• pinball loss
• elastic-net SVM
• data-driven selection
• vertical distribution
• asymmetry parameter

Innovation

• pinball loss
• elastic-net SVM
• data-driven parameter selection
• vertically distributed optimization
• variable-splitting solver