用贝叶斯自回归优化时间型马特恩核高斯过程超参数
Bayesian autoregression to optimize temporal Matérn kernel Gaussian process hyperparameters
- 将超参数优化转化为自回归模型的递归贝叶斯估计
- 运行时间更短，预测误差比边际似然最大化更低
- 适合需要高效高精度时间序列建模的研究者
高斯过程是概率数值计算领域的重要模型。本文提出一种针对时间型马特恩核高斯过程的超参数优化方法，将优化问题转化为自回归模型参数的递归贝叶斯估计。实验表明，该方法在运行时间和最终均方根误差方面均优于最大化边际似然及哈密顿蒙特卡洛采样，在高斯过程回归中表现更优。
原文摘要 · Abstract (English)
Gaussian processes are important models in the field of probabilistic numerics. We present a procedure for optimizing Matérn kernel temporal Gaussian processes with respect to the kernel covariance function's hyperparameters. It is based on casting the optimization problem as a recursive Bayesian estimation procedure for the parameters of an autoregressive model. We demonstrate that the proposed procedure outperforms maximizing the marginal likelihood as well as Hamiltonian Monte Carlo sampling, both in terms of runtime and ultimate root mean square error in Gaussian process regression.
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