Weighted Importance Sampling (WIS)

Implementation: crl.estimators.importance_sampling.WISEstimator

Assumptions

• Sequential ignorability
• Overlap/positivity

Requires

• LoggedBanditDataset or TrajectoryDataset
• behavior_action_probs for logged actions

Diagnostics to check

• overlap.support_violations
• ess.ess_ratio
• weights.tail_fraction

Formula

Self-normalized IS:

$\hat V = \frac{\sum_i w_i G_i}{\sum_i w_i}$.

Uncertainty

• Normal-approximation CI by default.
• Bootstrap CI available via bootstrap=True.

Failure modes

• Bias from normalization in small samples.
• Heavy-tailed ratios can still dominate variance.

Minimal example

from crl.estimators.importance_sampling import WISEstimator

report = WISEstimator(estimand, clip_rho=10.0).estimate(dataset)

References

• Swaminathan & Joachims (2015)