ols_get_stats: OLS Gradient and Hessian

In ipd: Inference on Predicted Data

OLS Gradient and Hessian

Description

Computes the statistics needed for the OLS-based prediction-powered inference.

Usage

ols_get_stats(
  est,
  X_l,
  Y_l,
  f_l,
  X_u,
  f_u,
  w_l = NULL,
  w_u = NULL,
  use_u = TRUE
)

Arguments

est	(vector): Point estimates of the coefficients.
X_l	(matrix): Covariates for the labeled data set.
Y_l	(vector): Labels for the labeled data set.
f_l	(vector): Predictions for the labeled data set.
X_u	(matrix): Covariates for the unlabeled data set.
f_u	(vector): Predictions for the unlabeled data set.
w_l	(vector, optional): Sample weights for the labeled data set.
w_u	(vector, optional): Sample weights for the unlabeled data set.
use_u	(boolean, optional): Whether to use the unlabeled data set.

Value

(list): A list containing the following:

grads

(matrix): n x p matrix gradient of the loss function with respect to the coefficients.

grads_hat

(matrix): n x p matrix gradient of the loss function with respect to the coefficients, evaluated using the labeled predictions.

grads_hat_unlabeled

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

inv_hessian

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

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, use_u = TRUE)

ipd documentation built on April 4, 2025, 4:41 a.m.