Estimate_GP_params: Estimate parameters from fast computation of GaSP model

In SKFCPD: Fast Online Changepoint Detection for Temporally Correlated Data

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

SKFCPD documentation built on June 22, 2024, 11:06 a.m.