optimal_subsample.R

N <- 1000
x1 <- 5*rnorm(n=N)
x2 <- 2*rnorm(n=N)
y <- x1 + x2 + rnorm(n=N)
# full data
df <- tibble(group = 'a', y, x1, x2)

# sample data to get "pilot estimators"
tau = 0.5
df_sample <- df |> sample_frac(.10)
fit <- rq(y ~ x1 + x2 - 1, tau = tau, data = df_sample)

# use weights from the small model to predict the outcomes from the full data
df_example <- df |> mutate(y_hat = predict(fit, df)) |>
  mutate( 
            e = y - y_hat,
            indicator = ifelse(e < 0, 1, 0),
            magnitude_x = sqrt(rowSums(across(c(x1, x2))^2)), # square the features, sum, then root
            weight = abs(tau - indicator) * magnitude_x,
            normalized_weight_pi_lopt_beta = weight / sum(weight)
          )

df_example |>
  write_csv('df_subsample_calculation_example.csv')