These related topics some of which might be represented in this workshop: (1) imprecise probabilities, (2) prequential statistics, (3) on-line prediction, (4) algorithmic randomness, and (5) conformal prediction.
- Imprecise probabilities (see www.sipta.org) is now a fairly broad field, which includes Walley's upper and lower probabilities, Dempster-Shafer theory, and other approaches to loosening the classical axioms of probability. The imprecise-probabilities community has accumulated expertise in studying various classes of set functions, including several important classes of Choquet capacities. Inasmuch as game-theoretic probability leads to upper and lower probabilities for events, it can be considered a topic within imprecise probabilities, and the extent to which other work on imprecise probabilities can be understood game-theoretically is an interesting and sometimes open question.
- Philip Dawid introduced prequential ("predictive sequential") statistics in the 1980s. It helped inspire the development of game-theoretic probability in the 1990s, because it re-conceptualized the notion of a probability distribution for a sequence of events as a strategy for a forecaster in a sequential forecasting game, which the forecaster can also play without thinking through a complete strategy. It has recently attracted renewed attention, because it brings statistics closer to the spirit of machine learning, shifting emphasis from parameter estimation and model selection to predictive performance.
- On-line prediction is a computer-science counterpart of prequential statistics. Performance of prediction strategies is measured either by evaluating a loss function or by measuring calibration and resolution. There are three important recent threads in on-line prediction: (i) prediction with expert advice, (ii) well-calibrated prediction, and (iii) defensive forecasting. All three are related to game-theoretic probability, and an elucidation of the relation may help the three learn from each other.
- The algorithmic theory of randomness, which continues to develop, shares with game-theoretic probability roots in the pioneering work by Ville in the 1930s and Schnorr in the 1970s. It still provides a theoretical underpinning and a convenient testbed for game-theoretic probability and its applications. It also contributes to prequential statistics, on-line prediction, and conformal prediction. This workshop will help the number of connections, already significant, to grow further.
- Conformal prediction is a method of producing prediction sets that can be applied on top of a wide range of prediction algorithms. The method has a guaranteed coverage probability under the standard IID assumption regardless of whether the assumptions (often considerably more restrictive) of the underlying algorithm are satisfied. The method shares the origins and techniques with game-theoretic probability and algorithmic randomness. There are annual workshops on conformal prediction (third planned for October 2014) for discussing applied aspects of conformal prediction. Recent theoretical work has included the analysis of the method of "conformalizing" for Bayesian algorithms. For the method to be really useful it is desirable that in the case where the assumptions of the underlying algorithm are satisfied, the conformal predictor loses little in efficiency as compared with the underlying algorithm (whereas being a conformal predictor, it has the stronger guarantee of validity). Asymptotic results have been obtained for Bayesian ridge regression, and work is underway for other classes of prediction algorithms. This workshop might serve as a forum for discussing new results and approaches in theoretical conformal prediction.