FastGaSP (version 0.6.0)

gppca: Setting up the GPPCA model

Description

Creating an gppca class for generalized probabilistic principal component analysis of correlated data.

Usage

gppca(input,output, d, est_d=FALSE, shared_params=TRUE, kernel_type="matern_5_2")

Value

gppca returns an S4 object of class gppca.

Arguments

input

a vector for the sorted input locations. The length is equal to the number of observations.

output

a k*d matrix for the observations at the sorted input locations. Here k is the number of locations and n is the number of observations.

d

number of latent factors.

est_d

a bool value, default is FALSE. If TRUE, d will be estimated by either variance matching (when noise level is given) or information criteria (when noise level is unknown). Otherwise, d is fixed, and users must assign a value to argument d.

shared_params

a bool value, default is TRUE. If TRUE, the latent processes share the correlation and variance parameters. Otherwise, each latent process has distinct parameters.

kernel_type

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

Author

tools:::Rd_package_author("FastGaSP") Maintainer: tools:::Rd_package_maintainer("FastGaSP")

References

Gu, M., & Shen, W. (2020), Generalized probabilistic principal component analysis of correlated data, Journal of Machine Learning Research, 21(13), 1-41.

Examples

library(FastGaSP)
library(rstiefel)

matern_5_2_funct <- function(d, beta_i) {
  cnst <- sqrt(5.0)
  matOnes <- matrix(1, nrow = nrow(d), ncol = ncol(d))
  result <- cnst * beta_i * d
  res <- (matOnes + result + (result^2) / 3) * exp(-result)
  return(res)
}

n=200
k=8
d=4

beta_real=0.01
sigma_real=1
sigma_0_real=sqrt(.01)
input=seq(1,n,1)
R0_00=as.matrix(abs(outer(input,input,'-')))
R_r = matern_5_2_funct(R0_00, beta_real)
L_sample = t(chol(R_r))
kernel_type='matern_5_2'


input=sort(input)
delta_x=input[2:length(input)]-input[1:(length(input)-1)]
A=rustiefel(k, d)  ##sample from Stiefel manifold
Factor=matrix(0,d,n)
for(i in 1: d){
  Factor[i,]=sigma_real^2*L_sample%*%rnorm(n)
}
output=A
  
##constucting the gppca.model
gppca_obj <- gppca(input, output, d, shared_params = TRUE,est_d=FALSE)