Multicalibrated Partitions for Importance Weights

Understand

The ratio between the probability that two distributions $R$ and $P$ give to points $x$ are known as importance weights or propensity scores and play a fundamental role in many different fields, most notably, statistics and machine learning.

• Among its applications, importance weights are central to domain adaptation, anomaly detection, and estimations of various divergences such as the KL divergence.
• We consider the common setting where $R$ and $P$ are only given through samples from each distribution.
• The vast literature on estimating importance weights is either heuristic, or makes strong assumptions about $R$ and $P$ or on the importance weights themselves.