ipd (version 0.1.4)

calc_lhat_glm: Estimate PPI++ Power Tuning Parameter

Description

Calculates the optimal value of lhat for the prediction-powered confidence interval for GLMs.

Usage

calc_lhat_glm(
  grads,
  grads_hat,
  grads_hat_unlabeled,
  inv_hessian,
  coord = NULL,
  clip = FALSE
)

Value

(float): Optimal value of lhat in [0,1].

Arguments

grads

(matrix): n x p matrix gradient of the loss function with respect to the parameter evaluated at the labeled data.

grads_hat

(matrix): n x p matrix gradient of the loss function with respect to the model parameter evaluated using predictions on the labeled data.

grads_hat_unlabeled

(matrix): N x p matrix gradient of the loss function with respect to the parameter evaluated using predictions on the unlabeled data.

inv_hessian

(matrix): p x p matrix inverse of the Hessian of the loss function with respect to the parameter.

coord

(int, optional): Coordinate for which to optimize lhat. If None, it optimizes the total variance over all coordinates. Must be in (1, ..., d) where d is the shape of the estimand.

clip

(boolean, optional): Whether to clip the value of lhat to be non-negative. Defaults to False.

Examples

dat <- simdat(model = "ols")

form <- Y - f ~ X1

X_l <- model.matrix(form, data = dat[dat$set_label == "labeled",])

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

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

X_u <- model.matrix(form, data = dat[dat$set_label == "unlabeled",])

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

est <- ppi_plusplus_ols_est(X_l, Y_l, f_l, X_u, f_u)

stats <- ols_get_stats(est, X_l, Y_l, f_l, X_u, f_u)

calc_lhat_glm(stats$grads, stats$grads_hat, stats$grads_hat_unlabeled,

  stats$inv_hessian, coord = NULL, clip = FALSE)