Multiculturality and multicalibration are the concepts of multigroup fairness in predictions that have discovered numerous applications in the complexity of learning and computation. They can be achieved from a single learning primitive primitive: learning weak agnosticism. Here we investigate the power of multi-layers as learning primitive, with or without additional assumptions of calibration. Multicasuality itself is rather weak, but we can see that adding global calibration (the concept called calibrated multiculturality) can significantly improve its power.
We present evidence that multiculturality may not be as powerful as standard weak agnostic learning, even if we assume that the best hypotheses are correlated to post-process multi-carit predictors to obtain weak learners. Rather, it shows that it generates a limited form of weak agnostic learning. However, by requiring the adjustment of predictors, it recovers not only weak but powerful agnostic learning. A similar image appears when we consider the derivation of hardcore measures from predictors that satisfy the concept of multigroup fairness. On the one hand, multiculturality produces only hardcore measurements of optimal density half the density, but it shows that calibrated multiculturality (of the weighted version) achieves optimal density. Our results provide new insight into the complementary roles of multicalculation and calibration in each setting. They shed light on why multi-layering and global calibration are not particularly strong, but why it brings a rather strong concept.
- †Oxford University
- ‡Stanford University
