ValidMLInference 0.0.9

RegLabels

ValidMLInference

This repository hosts the code for the ValidMLInference package, implementing bias corrction methods described in Battaglia, Christensen, Hansen & Sacher (2024). The two core functions are:

ols_bca

This procedure first computes the standard OLS estimator on a design matrix (Xhat), the first column of which contains AI/ML-generated binary labels, and then applies an additive correction based on an estimate (fpr) of the false-positive rate computed externally. The method also adjusts the variance estimator with a finite-sample correction term to account for the uncertainty in the bias estimation.

Parameters
----------
Y : array_like, shape (n,)
    Response variable vector.
Xhat : array_like, shape (n, d)
    Design matrix, the first column of which contains the AI/ML-generated binary covariates.
fpr : float
    False positive rate of misclassification, used to correct the OLS estimates.
m : int or float
    Size of the external sample used to estimate the classifier's false-positive rate. Can be set to 'inf' when the false-positive rate is known exactly.

Returns
-------
b : ndarray, shape (d,)
    Bias-corrected regression coefficient estimates.
V : ndarray, shape (d, d)
    Adjusted variance-covariance matrix for the bias-corrected estimator.

one_step_unlabeled

This method jointly estimates the upstream (measurement) and downstream (regression) models using only the unlabeled likelihood. Leveraging JAX for automatic differentiation and optimization, it minimizes the negative log-likelihood to obtain the regression coefficients. The variance is then approximated via the inverse Hessian at the optimum.

Parameters
----------
Y : array_like, shape (n,)
    Response variable vector.
Xhat : array_like, shape (n, d)
    Design matrix constructed from AI/ML-generated regressors.
homoskedastic : bool, optional (default: False)
    If True, assumes a common error variance; otherwise, separate error variances are estimated.
distribution : allows to specify the distribution of error terms, optional. By default, it's Normal(0,1).
    A custom distribution can be passed down as any jax-compatible PDF function that takes inputs (x, loc, scale).

Returns
-------
b : ndarray, shape (d,)
    Estimated regression coefficients extracted from the optimized parameter vector.
V : ndarray, shape (d, d)
    Estimated variance-covariance matrix for the regression coefficients, computed as the inverse 
    of the Hessian of the objective function.