Local, algebraic simplifications of Gaussian random fields
Local, algebraic simplifications of Gaussian random fields
复制标题
高斯随机场的局部代数简化
DOI:
10.1088/1475-7516/2018/12/022
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发表时间:
2018
影响因子:
6.4
通讯作者:
Bjorkmo T
中科院分区:
文献类型:
--
作者:
Bjorkmo T
Many applications of Gaussian random fields and Gaussian random processes are limited by the computational complexity of evaluating the probability density function, which involves inverting the relevant covariance matrix. In this work, we show how that problem can be completely circumvented for the local Taylor coefficients of a Gaussian random field with a Gaussian (orsquare exponential') covariance function. Our results hold for any dimension of the field and to any order in the Taylor expansion. We present two applications. First, we show that this method can be used to explicitly generate non-trivial potential energy landscapes with many fields. This application is particularly useful when one is concerned with the field locally around special points (eg maxima or minima), as we exemplify by the problem of cosmicmanyfield'inflation in the early universe. Second, we show that this method has applications in machine learning, and greatly simplifies the regression problem of determining the hyperparameters of the covariance function given a training data set consisting of local Taylor coefficients at single point. An accompanying Mathematica notebook is available at\href {https://doi. org/10.17863/CAM. 22859}{https://doi. org/10.17863/CAM. 22859}.
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DOI:
--
发表时间:
--
期刊:
影响因子:
--
作者:
A. Ghobadi;Matthew S. Holt;Julie K. Ritchey;J. Dipersio
通讯作者:
J. Dipersio
影响因子:
6.4
作者:
Bjorkmo T
通讯作者:
Bjorkmo T
影响因子:
8.6
作者:
David Mulryne
通讯作者:
David Mulryne
DOI:
--
发表时间:
2011
期刊:
影响因子:
--
作者:
J. Frazer;A. Liddle
通讯作者:
A. Liddle
影响因子:
5.4
作者:
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通讯作者:
J. Schwandt