{"title":"拟牛顿BFGS方法的随机标度改进高斯过程中协方差矩阵逆的O(N2)运算逼近","authors":"Yunong Zhang, W. Leithead, D. Leith","doi":"10.1109/ISIC.2007.4450928","DOIUrl":null,"url":null,"abstract":"Gaussian process (GP) is a Bayesian nonparametric regression model, showing good performance in various applications. Similar to other computational models, Gaussian process frequently encounters the matrix-inverse problem during its model-tuning procedure. The matrix inversion is generally of O(N3) operations where N is the matrix dimension. We proposed using the O(N2)-operation quasi-Newton BFGS method to approximate/replace the exact inverse of covariance matrix in the GP context. As inspired during a paper revision, in this paper we show that by using the random-scaling technique, the accuracy and effectiveness of such a BFGS matrix-inverse approximation could be further improved. These random-scaling BFGS techniques could be widely generalized to other machine-learning systems which rely on explicit matrix-inverse.","PeriodicalId":184867,"journal":{"name":"2007 IEEE 22nd International Symposium on Intelligent Control","volume":"10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Random Scaling of Quasi-Newton BFGS Method to Improve the O(N2)-operation Approximation of Covariance-matrix Inverse in Gaussian Process\",\"authors\":\"Yunong Zhang, W. Leithead, D. Leith\",\"doi\":\"10.1109/ISIC.2007.4450928\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Gaussian process (GP) is a Bayesian nonparametric regression model, showing good performance in various applications. Similar to other computational models, Gaussian process frequently encounters the matrix-inverse problem during its model-tuning procedure. The matrix inversion is generally of O(N3) operations where N is the matrix dimension. We proposed using the O(N2)-operation quasi-Newton BFGS method to approximate/replace the exact inverse of covariance matrix in the GP context. As inspired during a paper revision, in this paper we show that by using the random-scaling technique, the accuracy and effectiveness of such a BFGS matrix-inverse approximation could be further improved. These random-scaling BFGS techniques could be widely generalized to other machine-learning systems which rely on explicit matrix-inverse.\",\"PeriodicalId\":184867,\"journal\":{\"name\":\"2007 IEEE 22nd International Symposium on Intelligent Control\",\"volume\":\"10 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2007 IEEE 22nd International Symposium on Intelligent Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIC.2007.4450928\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2007 IEEE 22nd International Symposium on Intelligent Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIC.2007.4450928","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Random Scaling of Quasi-Newton BFGS Method to Improve the O(N2)-operation Approximation of Covariance-matrix Inverse in Gaussian Process
Gaussian process (GP) is a Bayesian nonparametric regression model, showing good performance in various applications. Similar to other computational models, Gaussian process frequently encounters the matrix-inverse problem during its model-tuning procedure. The matrix inversion is generally of O(N3) operations where N is the matrix dimension. We proposed using the O(N2)-operation quasi-Newton BFGS method to approximate/replace the exact inverse of covariance matrix in the GP context. As inspired during a paper revision, in this paper we show that by using the random-scaling technique, the accuracy and effectiveness of such a BFGS matrix-inverse approximation could be further improved. These random-scaling BFGS techniques could be widely generalized to other machine-learning systems which rely on explicit matrix-inverse.