Calibration via Regression

In the online prediction setting, the concept of calibration entails having the empirical (conditional) frequencies match the claimed predicted probabilities. This contrasts with more traditional online prediction goals of getting a low cumulative loss. The differences between these goals have typically made them hard to compare with each other. This paper shows how to get an approximate form of calibration out of a traditional online loss minimization algorithm, namely online regression. As a corollary, we show how to construct calibrated forecasts on a collection of subsequences.