Baselines

library(kpe)

In addition to kpe(), the package provides two baseline estimators of the personalization effect: train_eval() and papd().

Prerequisites

See vignette("getting-started", package = "kpe") for installation and the full learner/backend table. The runnable comparison at the end uses only base-R learners ("linear", "simple"), so it needs no extra packages; the policy_tree/random_forest calls shown for illustration are not evaluated, but running them would require policytree, ranger, and glmnet.

train_eval()

res <- train_eval(X, A, Y, propensity,
                  n_shuffles        = 100,
                  contextual_policy = "policy_tree",
                  best_arm          = "ips",
                  reward_model      = "random_forest",
                  seed              = 0)

Inputs. Identical to kpe(). The n_folds argument is accepted for symmetry and is ignored.

Output. An S3 list of class "kpe". policy_stability and overall_stability are returned as NaN because each shuffle evaluates a different randomly-chosen held-out half, so per-sample policy agreement across shuffles is not well-defined.

Computation. On each of n_shuffles random 50/50 splits of the data, the reward, contextual-policy, and best-arm learners are estimated on one half and the AIPW influence function of Eq. S17 is evaluated on the other half. The Algorithm-1 variance decomposition is applied to the per-shuffle (psi_hat, sigma_hat) pairs using n / 2 as the effective sample size for the t-test denominator.

papd()

res <- papd(X, A, Y, propensity,
            n_shuffles        = 100,
            contextual_policy = "policy_tree",
            best_arm          = "ips",
            seed              = 0)

Inputs. Identical to kpe(). The n_folds and reward_model arguments are accepted for symmetry and are ignored; papd() always uses 3 folds and does not fit a reward model.

Output. An S3 list of class "kpe".

Computation. Implementation of the Population Average Prescriptive Difference of Imai and Li (2023), specialized to the case where one policy class is restricted to providing a single best arm for all individuals, as described in Li and Brunskill (2026, Science, 2026). On each of n_shuffles random 3-fold partitions, the contextual policy and best-arm learner are trained on two folds and the test-fold-centered inverse-propensity statistic

$$\psi^{\text{PAPD}}_i = \frac{\mathbf{1}\{A = \pi(X), \pi_0 \neq \pi(X)\} - \mathbf{1}\{A = \pi_0, \pi_0 \neq \pi(X)\}} {p(A \mid X)}\,(Y_i - \bar Y_{\text{test}})$$

is computed on the held-out fold. The Algorithm-1 variance decomposition is applied to the per-shuffle (psi_hat, sigma_hat) pairs.

Side-by-side comparison on a synthetic dataset

set.seed(1)
n <- 400
X <- matrix(runif(n * 2, -1, 1), ncol = 2)
A <- rbinom(n, 1, 0.5)
Y <- ifelse(X[, 1] >= 0, A, 0.5 * (1 - A)) + rnorm(n, sd = 0.3)

common <- list(
  propensity        = 0.5,
  n_shuffles        = 10,
  contextual_policy = "linear",
  best_arm          = "simple",
  reward_model      = "linear",
  seed              = 0
)
r_kpe  <- do.call(kpe,        c(list(X = X, A = A, Y = Y), common))
r_trev <- do.call(train_eval, c(list(X = X, A = A, Y = Y), common))
r_papd <- do.call(papd,       c(list(X = X, A = A, Y = Y), common))

summary_row <- function(r) {
  ci <- r$confidence_interval
  data.frame(method  = r$method,
             psi     = r$psi,
             ci_lo   = ci[1],
             ci_hi   = ci[2],
             p_value = r$p_value)
}
do.call(rbind, lapply(list(r_kpe, r_trev, r_papd), summary_row))

##       method       psi     ci_lo     ci_hi      p_value
## 1        kpe 0.1995672 0.1511233 0.2480111 4.053638e-15
## 2 train_eval 0.2009647 0.1306704 0.2712589 3.469744e-08
## 3       papd 0.1919487 0.1441637 0.2397337 1.651229e-14