On calibration error of randomizing forecastind algorithms

Vladimir V'yugin

Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow
Wednesday 16 May 2007 (219 McCrea Building, 1pm)

Recently, it was shown that calibration with an error less than $\delta>0$ is almost surely guaranteed with a randomized forecasting algorithm, where forecasts are chosen using randomized rounding up to $\delta$ of deterministic forecasts. We show that this error can not be improved for a large majority of sequences generated by a probabilistic algorithm: we prove that combining outcomes of coin-tossing and a transducer algorithm, it is possible to effectively generate with probability close to one a sequence ``resistant'' to any randomized rounding forecasting with an error much smaller than $\delta$. According to Dawid's prequential framework, we consider partial randomized forecasting algorithms defined on all initial fragments of a given sequence of outcomes; these algorithms can be undefined outside this sequence.