In udellgroup/mixedgcImp: Missing value imputation for mixed data through Gaussian copula

knitr::opts_chunk$set(echo = TRUE)

\newcommand{\bX}{\mathbf{X}} \newcommand{\bZ}{\mathbf{Z}} \newcommand{\bx}{\mathbf{x}} \newcommand{\bz}{\mathbf{z}} \newcommand{\bigf}{\mathbf{f}} \newcommand{\bo}{\mathbf{0}}

Generate data

We generate the high rank continuous data matrix $\bX\in \mathbb{R}^{500\times200}$ from a low rank Gaussian copula as in the experiments of https://arxiv.org/pdf/2006.10829.pdf and randomly mask $40\%$ observation as test set.

  p = 200
  n = 500
  rank = 10
  sigma = 0.1
  set.seed(410)
  W = matrix(rnorm(p*rank), nrow = p)
  W = t(apply(W, 1, function(x){x/sqrt(sum(x^2))  * sqrt((1-sigma))}))
  Z = matrix(rnorm(n*rank), ncol = rank) %*% t(W) + matrix(rnorm(n*p, sd = sqrt(sigma)), ncol = p)
  # cubic transformation
  X = Z^3
  # mask 40% of the original observation
  X_obs = X
  loc = sample(1:prod(n*p), size = floor(prod(n*p)*0.4))
  X_obs[loc] = NA

Fitting low rank Gaussian copula

Simply specify the rank to the function call.

library(gcimputeR)
est = impute_mixedgc_ppca(X_obs, rank = 10) # around 8 secs
print("Normalized root mean squared error (NRMSE) is: ")
print(sqrt(mean((est$Ximp[loc] - X[loc])^2))/sqrt(mean(X[loc]^2)))

Construct confidence interval

ct = ct_impute(X_obs, est, 0.95)
print("The empirical coverage is: ")
print(mean(X[loc] >= ct$lower[loc] & X[loc] <= ct$upper[loc]))
print("The mean confidence interval length is: ")
mean(ct$upper[loc] - ct$lower[loc])

udellgroup/mixedgcImp documentation built on Jan. 25, 2023, 7:55 p.m.