基于拉普拉斯方法的大规模高斯过程分类算法  

Large-scale Gaussian process classification via Laplace's method

作　　者：马彪[1] 贺建军[1,2] 李厚杰[1] 

机构地区：[1]大连民族大学信息与通信工程学院,辽宁大连116600 [2]大连理工大学电子信息与电气工程学部,辽宁大连116024

出　　处：《控制与决策》2017年第7期1319-1324,共6页Control and Decision

基　　金：国家自然科学基金项目(61503058;61374170);辽宁省自然科学基金项目(201602190;2015020084;2015020099);辽宁省教育厅科学技术研究项目(L2014540;L2015127);大连市青年科技之星项目(2016RQ072);中央高校基本科研业务费专项资金项目(DC201501055;DC201501060201)

摘　　要：基于KL散度的大规模变分高斯过程分类算法(KLSP)需要同时对诱导变量的均值向量和协方差矩阵进行优化,这会给模型求解带来一定的挑战.基于拉普拉斯方法建立一种改进算法:首先为诱导变量的后验分布构造一个易于计算的下界;然后利用拉普拉斯方法计算该下界的一个高斯逼近作为诱导变量的后验分布函数的近似表达式,将问题转换为一个只与均值向量有关的凸优化问题,从而降低了模型的求解难度.仿真实验结果表明,所提出的改进算法在速度和精度上都较原始算法有了明显提高.Scalable variational Gaussian process classification based on KL divergence（KLSP） is generaly plagued by the fact that both the mean and covariance matrix of inducing variables need to be optimized, therefore an improved algorithm is proposed by using the Laplace＇s method. Firstly, a lower bound of the posterior distribution of inducing variables is constructed, which can be computed easily. Then a Gaussian approximation of this lower bound is computed, which is by using the Laplace＇s method taken as the approximation the posterior distribution of inducing variables. As a result,the objective function of the proposed algorithm is a concave function with respect to the mean of inducing variables only, which can be solved easily. The experimental results show that, compared with the original algorithm, the speed and accuracy of the proposed algorithm are improved obviously.

关 键 词：大规模数据分类 高斯过程模型 拉普拉斯方法 变分方法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]