gppca: Setting up the GPPCA model

In FastGaSP: Fast and Exact Computation of Gaussian Stochastic Process

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")

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.

Value

gppca returns an S4 object of class gppca.

Author(s)

Mengyang Gu [aut, cre], Xinyi Fang [aut], Yizi Lin [aut] Maintainer: Mengyang Gu <[e-mail]>

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)

FastGaSP documentation built on April 4, 2025, 5:16 a.m.