融合概率分布和单调性的支持向量回归算法
Improved support vector regression algorithm combining with probability distribution and monotone property

传统支持向量回归是单纯基于样本数据的输入输出值建模, 仅使用样本数据信息, 未充分利用其他已知信 息, 模型泛化能力不强. 为了进一步提高其性能, 提出一种融合概率分布和单调性先验知识的支持向量回归算法. 首先将对偶二次规划问题简化为线性规划问题, 在求解时，加入与拉格朗日乘子相关的单调性约束条件; 通过粒 子群算法优化惩罚参数和核参数, 优化目标包括四阶矩估计表示的输出样本概率分布特性. 实验结果表明, 融合这 两部分信息的模型, 能使预测值较好地满足训练样本隐含的概率分布特性及已知的单调性, 既提高了预测精度, 又 增加了模型的可解释性.
The traditional support vector regression (SVR) is only based on data information, and a great deal of prior knowledge is neglected. In order to improve its performance, a new SVR algorithm combining with probability distribution and monotone property is proposed. Firstly, the dual quadratic programming problem is simplified as a linear one. Secondly, the monotonic constraints associated with Lagrange multiplier are added. Thirdly, the particle swarm optimization (PSO) is employed to optimize the penalty and kernel parameters. And the fitness function of PSO is the deviation of the probability distribution estimated by four-order moments. The experiment results show that the performance of the proposed SVR model is improved and the developed model satisfies probability distribution and monotone property.