Estimate_GP_params {SKFCPD}

Estimate parameters from fast computation of GaSP model

Description

Getting the estimated parameters from fast computation of the Gaussian stochastic process (GaSP) model with the Matern kernel function with a noise.

Usage

  Estimate_GP_params(input, output, kernel_type='matern_5_2')

Arguments

input

a vector with dimension num_obs x 1 for the sorted input locations.

output

a vector with dimension n x 1 for the observations at the sorted input locations.

kernel_type

a character to specify the type of kernel to use. The current version supports kernel_type to be "matern_5_2" or "exp", meaning that the matern kernel with roughness parameter being 2.5 or 0.5 (power exponent kernel), respectively.

Value

Estimate_GP_params returns an S4 object of class Estimated_GP_params with estimated parameters including

beta

the inverse range parameter, i.e. beta=1/gamma

eta

the noise-to-signal ratio

sigma_2

the variance parameter

Author(s)

Hanmo Li [aut, cre], Yuedong Wang [aut], Mengyang Gu [aut]

Maintainer: Hanmo Li <[e-mail]>

References

Hartikainen, Jouni, and Simo Sarkka. Kalman filtering and smoothing solutions to temporal Gaussian process regression models. In 2010 IEEE international workshop on machine learning for signal processing, pp. 379-384. IEEE, 2010.

Gu, Mengyang, and Yanxun Xu. Fast nonseparable Gaussian stochastic process with application to methylation level interpolation. Journal of Computational and Graphical Statistics 29, no. 2 (2020): 250-260.

Gu, Mengyang, and Weining Shen. Generalized probabilistic principal component analysis of correlated data. The Journal of Machine Learning Research 21, no. 1 (2020): 428-468.

Gu, Mengyang, Xiaojing Wang, and James O. Berger. Robust Gaussian stochastic process emulation. The Annals of Statistics 46, no. 6A (2018): 3038-3066.

Examples

  library(SKFCPD)

  #------------------------------------------------------------------------------
  # simple example with noise
  #------------------------------------------------------------------------------
  
  y_R<-function(x){
    cos(2*pi*x)
  }
  ###let's test for 100 observations
  set.seed(1)
  num_obs=100
  input=runif(num_obs)
  output=y_R(input)+rnorm(num_obs,mean=0,sd=1)
  
  ## run Estimate_GP_params to get estimated parameters
  params_est = Estimate_GP_params(input, output)
  print(params_est@beta) ## inverse of range parameter
  print(params_est@eta) ## noise-to-signal ratio
  print(params_est@sigma_2) ## variance