predict.gppca,gppca-method: Prediction and uncertainty quantification on the future...

In FastGaSP: Fast and Exact Computation of Gaussian Stochastic Process

Prediction and uncertainty quantification on the future observations using GPPCA.

Description

This function predicts the future observations using a GPPCA model. Uncertainty quantification is available.

Usage

## S4 method for signature 'gppca'
predict.gppca(object, param, A_hat, step=1, interval=FALSE, interval_data=TRUE)

Arguments

object	an object of class gppca.
param	estimated parameters (beta, sigma2, sigma0_2).
A_hat	estimated factor loading matrix.
step	a vector. Number of steps to be predicted. Default is 1.
interval	a bool value, default is FALSE. If TRUE, the 95% predictive intervals are computed.
interval_data	a bool value, default is TRUE. If TRUE, the 95% predictive intervals of the observations are computed. Otherwise, the 95% predictive intervals of the mean of the observation are computed.

Value

pred_mean	the predictive mean.
pred_interval_95lb	the 95% lower bound of the interval.
pred_interval_95ub	the 95% upper bound of the interval.

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%*%Factor+matrix(rnorm(n*k,mean=0,sd=sigma_0_real),k,n)
  
##constucting the gppca.model
gppca_obj <- gppca(input, output, d, shared_params = TRUE,est_d=FALSE)
## estimate the parameters
gppca_fit <- fit.gppca(gppca_obj)

## two-step-ahead prediction
param <- c(gppca_fit$est_beta, gppca_fit$est_sigma2, gppca_fit$est_sigma0_2)
gppca_pred <- predict.gppca(gppca_obj, param, gppca_fit$est_A, step=1:3)
gppca_pred$pred_mean

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