Moment Multicalibration for Uncertainty Estimation
This work addresses the need for reliable uncertainty estimation and fairness assessment in predictive models across diverse subgroups, representing an incremental advancement by building on existing multicalibration concepts.
The paper tackles the problem of extending multicalibration beyond means to higher moments like variances, enabling regression functions to predict not only expectations but also higher moments of label distributions that are accurate across numerous finely defined subgroups. The result provides a principled method for uncertainty estimation and fairness diagnosis, with an application yielding marginal prediction intervals valid across all sufficiently large subgroups.
We show how to achieve the notion of "multicalibration" from Hébert-Johnson et al. [2018] not just for means, but also for variances and other higher moments. Informally, it means that we can find regression functions which, given a data point, can make point predictions not just for the expectation of its label, but for higher moments of its label distribution as well-and those predictions match the true distribution quantities when averaged not just over the population as a whole, but also when averaged over an enormous number of finely defined subgroups. It yields a principled way to estimate the uncertainty of predictions on many different subgroups-and to diagnose potential sources of unfairness in the predictive power of features across subgroups. As an application, we show that our moment estimates can be used to derive marginal prediction intervals that are simultaneously valid as averaged over all of the (sufficiently large) subgroups for which moment multicalibration has been obtained.