Liu Huan, Tu Jiankai, Li Chunguang
College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China.
Entropy (Basel). 2022 Oct 31;24(11):1567. doi: 10.3390/e24111567.
Ordinal regression methods are widely used to predict the ordered labels of data, among which support vector ordinal regression (SVOR) methods are popular because of their good generalization. In many realistic circumstances, data are collected by a distributed network. In order to protect privacy or due to some practical constraints, data cannot be transmitted to a center for processing. However, as far as we know, existing SVOR methods are all centralized. In the above situations, centralized methods are inapplicable, and distributed methods are more suitable choices. In this paper, we propose a distributed SVOR (dSVOR) algorithm. First, we formulate a constrained optimization problem for SVOR in distributed circumstances. Since there are some difficulties in solving the problem with classical methods, we used the random approximation method and the hinge loss function to transform the problem into a convex optimization problem with constraints. Then, we propose subgradient-based algorithm dSVOR to solve it. To illustrate the effectiveness, we theoretically analyze the consensus and convergence of the proposed method, and conduct experiments on both synthetic data and a real-world example. The experimental results show that the proposed dSVOR could achieve close performance to that of the corresponding centralized method, which needs all the data to be collected together.
序数回归方法被广泛用于预测数据的有序标签，其中支持向量序数回归（SVOR）方法因其良好的泛化能力而受到欢迎。在许多实际情况中，数据是通过分布式网络收集的。为了保护隐私或由于一些实际限制，数据不能传输到中心进行处理。然而，据我们所知，现有的SVOR方法都是集中式的。在上述情况下，集中式方法不适用，分布式方法是更合适的选择。在本文中，我们提出了一种分布式SVOR（dSVOR）算法。首先，我们为分布式环境下的SVOR制定了一个约束优化问题。由于用经典方法解决该问题存在一些困难，我们使用随机逼近方法和铰链损失函数将该问题转化为一个带约束的凸优化问题。然后，我们提出基于次梯度的算法dSVOR来解决它。为了说明有效性，我们从理论上分析了所提方法的一致性和收敛性，并在合成数据和一个实际例子上进行了实验。实验结果表明，所提的dSVOR能够取得与相应集中式方法相近的性能，而集中式方法需要将所有数据收集在一起。
