sim_code/section_3/unbalanced/method_3.R

In RobinMDunn/ConformalTwoLayer: Distribution-Free Prediction Sets for Two-Layer Hierarchical Data

# Simulate unsupervised method 3, for case where we have k unbalanced groups.
# n_small = 5 observations for k-1 groups, n_large = 1000 observations for 1 group.
#
# DATA GENERATION:
# The observation from group j (j = 1, ..., k) is distributed as
#    Y_ji = theta_j + epsilon_ji (i = 1, ..., n_j)
#    theta_j ~ N(0, tau^2 = 100)
#    epsilon_ji ~ N(0, sigma^2 = 0.1)
# Vary k from 20 to 100 in increments of 5.

library(R.utils)
library(progress)
library(data.table)
library(ConformalTwoLayer)

# Read in arguments for start/end k (number of groups) and
# number of observations for small and large groups
start_k <- 20
end_k <- 100
n_small <- 5
n_large <- 1000

args <- commandArgs(trailingOnly = TRUE)
if (length(args) > 0) {
  args <- as.numeric(args)
  start_k <- args[1]
  end_k <- args[2]
  n_small <- args[3]
  n_large <- args[4]
}

# Set alpha level
alpha <- 0.1

# Construct vector of k values
all_k <- seq(20, 100, by = 5)

k_vec <- all_k[start_k <= all_k & all_k <= end_k]

# Construct data frame to store results
results <- data.table(k = k_vec,
                      n_small = n_small,
                      n_large = n_large,
                      coverage = NA_real_,
                      avg_length = NA_real_)

# Number of simulations to perform at each combination of k, n, and tau_sq
n_sim <- 1000

# Number of times to resample to get average p-value
n_resamp <- 100

# Set up progress bar
pb <- progress_bar$new(format = paste0("sim :current / :total [:bar] :eta"),
                       total = n_sim * length(k_vec), clear = T,
                       show_after = 0)

# For each k, repeat n_sim times:
# Simulate data, construct prediction interval,
# check whether new observation is inside interval.
for(row in 1:nrow(results)) {

  # Vectors to store coverage and prediction interval lengths
  covered_2alpha <- rep(NA, n_sim)

  pi_length_2alpha <- rep(NA, n_sim)

  # Extract k
  k_val <- results[row, k]

  # Keep coverage and length as NA unless k > 2/alpha - 1
  if(k_val > 2 / alpha - 1) {

    for(sim in 1:n_sim) {

      # Increment progress bar
      pb$tick()

      # Simulate data
      Y <- unsup_generate_data(k = k_val,
                               n_vec = c(rep(n_small, times = k_val - 1), n_large),
                               mu = 0, tau_sq = 100, sigma_sq = 0.1)

      # Generate a single new observation from a new group
      new_Y <- unsup_generate_data(k = 1, n_vec = 1, mu = 0, tau_sq = 100,
                                   sigma_sq = 0.1)

      # Construct prediction set and check whether new_Y is in set
      unsup_repeated_results <-
        unsup_repeated_subsample(Y = Y, alpha = alpha, k_val = k_val,
                                 n_resamp = n_resamp, new_Y = new_Y)

      # Check whether new observation is inside interval
      covered_2alpha[sim] <- unsup_repeated_results$covered

      # Store length of interval
      pi_length_2alpha[sim] <- unsup_repeated_results$pred_int_size

    }

    # Store coverage proportion
    results[row, coverage := mean(covered_2alpha)]

    # Store average prediction interval length
    results[row, avg_length := mean(pi_length_2alpha)]

  }

}

# Save simulation results. Label with n_small, n_large, k values.
fwrite(results,
       file = paste0("sim_data/section_3/unbalanced/method_3_small_",
                     n_small, "_large_", n_large, "_",
                     start_k, "_", end_k, ".csv"))