Probabilistic prediction and context tree identification in the Goalkeeper game

Abstract

Abstract In this article we address two related issues on the learning of probabilistic sequences of events. First, which features make the sequence of events generated by a stochastic chain more difficult to predict. Second, how to model the procedures employed by different learners to identify the structure of sequences of events. Playing the role of a goalkeeper in a video game, participants were told to predict step by step the successive directions—left, center or right—to which the penalty kicker would send the ball. The sequence of kicks was driven by a stochastic chain with memory of variable length. Results showed that at least three features play a role in the first issue: (1) the shape of the context tree summarizing the dependencies between present and past directions; (2) the entropy of the stochastic chain used to generate the sequences of events; (3) the existence or not of a deterministic periodic sequence underlying the sequences of events. Moreover, evidence suggests that best learners rely less on their own past choices to identify the structure of the sequences of events.

Keywords

• Statistical learning
• Probabilistic sequences
• Context tree models
• Probability matching
• Probability maximizing