pod.predict_local_std

predict_local_std(X, residuals, X_eval, bandwidth)

Estimates the local standard deviation using Gaussian Kernel Smoothing.

This implements a Nadaraya-Watson estimator ([M25] Eq. 2.9-2.11) for the squared residuals, to model how noise varies across the input domain (heteroscedasticity).

[digiqual] With several inputs, each input is first divided by its standard deviation in X, so one bandwidth (in standard deviations) treats all inputs alike regardless of their units. [M25] used a single input, where this only rescales the bandwidth.