ipd (version 0.1.4)

ppi_plusplus_ols: PPI++ OLS

Description

Helper function for PPI++ OLS estimation

Usage

ppi_plusplus_ols(
  X_l,
  Y_l,
  f_l,
  X_u,
  f_u,
  lhat = NULL,
  coord = NULL,
  w_l = NULL,
  w_u = NULL
)

Value

(list): A list containing the following:

est

(vector): vector of PPI++ OLS regression coefficient estimates.

se

(vector): vector of standard errors of the coefficients.

lambda

(float): estimated power-tuning parameter.

rectifier_est

(vector): vector of the rectifier OLS regression coefficient estimates.

var_u

(matrix): covariance matrix for the gradients in the unlabeled data.

var_l

(matrix): covariance matrix for the gradients in the labeled data.

grads

(matrix): matrix of gradients for the labeled data.

grads_hat_unlabeled

(matrix): matrix of predicted gradients for the unlabeled data.

grads_hat

(matrix): matrix of predicted gradients for the labeled data.

inv_hessian

(matrix): inverse Hessian matrix.

Arguments

X_l

(matrix): n x p matrix of covariates in the labeled data.

Y_l

(vector): n-vector of labeled outcomes.

f_l

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

X_u

(matrix): N x p matrix of covariates in the unlabeled data.

f_u

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

lhat

(float, optional): Power-tuning parameter (see https://arxiv.org/abs/2311.01453). The default value, NULL, will estimate the optimal value from the data. Setting lhat = 1 recovers PPI with no power tuning, and setting lhat = 0 recovers the classical point estimate.

coord

(int, optional): Coordinate for which to optimize lhat = 1. If NULL, it optimizes the total variance over all coordinates. Must be in (1, ..., d) where d is the dimension of the estimand.

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.

Details

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

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)

ppi_plusplus_ols(X_l, Y_l, f_l, X_u, f_u)