PPI++ Quantile Estimation

Helper function for PPI++ quantile estimation

Usage

ppi_plusplus_quantile(
  Y_l,
  f_l,
  f_u,
  q,
  alpha = 0.05,
  exact_grid = FALSE,
  w_l = NULL,
  w_u = NULL
)

Arguments

Y_l

(vector): n-vector of labeled outcomes.

f_l

(vector): n-vector of predictions in the labeled data.

f_u

(vector): N-vector of predictions in the unlabeled data.

q

(float): Quantile to estimate. Must be in the range (0, 1).

alpha

(scalar): type I error rate for hypothesis testing - values in (0, 1); defaults to 0.05.

exact_grid

(bool, optional): Whether to compute the exact solution (TRUE) or an approximate solution based on a linearly spaced grid of 5000 values (FALSE).

w_l

(ndarray, optional): Sample weights for the labeled data set. Defaults to a vector of ones.

w_u

(ndarray, optional): Sample weights for the unlabeled data set. Defaults to a vector of ones.

Value

tuple: Lower and upper bounds of the prediction-powered confidence interval for the quantile.

Details

PPI++: Efficient Prediction Powered Inference (Angelopoulos et al., 2023) https://arxiv.org/abs/2311.01453

Examples

dat <- simdat(model = "quantile")

form <- Y - f ~ X1

Y_l <- dat[dat$set == "labeled", all.vars(form)[1]] |> matrix(ncol = 1)

f_l <- dat[dat$set == "labeled", all.vars(form)[2]] |> matrix(ncol = 1)

f_u <- dat[dat$set == "unlabeled", all.vars(form)[2]] |> matrix(ncol = 1)

ppi_plusplus_quantile(Y_l, f_l, f_u, q = 0.5)
#> [1] 0.7490598 1.2481513