fmou | R Documentation |
Creating an fmou
class for fmou, a latent factor model with a fixed or estimated orthogonal factor loading matrix, where each latent factor is modeled as an O-U (Ornstein-Uhlenbeck) process.
fmou(output, d, est_d=FALSE, est_U0=TRUE, est_sigma0_2=TRUE, U0=NULL, sigma0_2=NULL)
output |
a k*n observation matrix, where k is the length of observations at each time step and n is the number of time steps. |
d |
number of latent factors. |
est_d |
a bool value, default is |
est_U0 |
a bool value, default is |
est_sigma0_2 |
a bool value, default is |
U0 |
the fixed factor loading matrix. Users should assign a k*d matrix to it when |
sigma0_2 |
variance of noise. User should assign a value to it when |
fmou
returns an S4 object of class fmou
.
Mengyang Gu [aut, cre], Xinyi Fang [aut], Yizi Lin [aut]
Maintainer: Mengyang Gu <mengyang@pstat.ucsb.edu>
Lin, Y., Liu, X., Segall, P., & Gu, M. (2025). Fast data inversion for high-dimensional dynamical systems from noisy measurements. arXiv preprint arXiv:2501.01324.
## generate simulated data
library(FastGaSP)
library(rstiefel)
d = 5 # number of latent factors
k = 20 # length of observation at each time step
n = 100 # number time step
noise_level = 1 # variance of noise
U = rustiefel(k, k) # factor loading matrix
z = matrix(NA, d, n)
sigma_2 = runif(d, 0.5, 1)
rho = runif(d, 0.95, 1)
for(l in 1:d){
R = matrix(NA, n, n)
diag(R) = 1
for(ir in 1:n){
for(ic in 1:n){
R[ir, ic] = rho[l]^(abs(ir-ic)) * R[ir, ir]
}
}
R = (sigma_2[l]/(1-rho[l]^2) )* R
z[l, ] = t(chol(R)) %*% rnorm(n)
}
signal = U[,1:d] %*% z
y = signal + matrix(rnorm(n*k,mean=0,sd=sqrt(noise_level)),k,n)
##constucting the fmou.model
fmou.model=fmou(output=y, d=d, est_U0=TRUE, est_sigma0_2=TRUE)
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