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
)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. IfNone, 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.