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

Yunong Zhang, W. Leithead, D. Leith
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引用次数: 0

摘要

高斯过程(GP)是一种贝叶斯非参数回归模型,在各种应用中表现出良好的性能。与其他计算模型类似,高斯过程在模型调整过程中经常遇到矩阵逆问题。矩阵反演通常是O(N3)个操作,其中N是矩阵维数。我们提出了用O(N2)-运算拟牛顿BFGS方法来近似/替换GP环境下协方差矩阵的精确逆。在一篇论文的修改中,我们证明了通过使用随机缩放技术,可以进一步提高这种BFGS矩阵逆逼近的准确性和有效性。这些随机缩放BFGS技术可以广泛推广到其他依赖显式矩阵逆的机器学习系统。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.
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