Learning from Games: Inductive Bias and Bayesian Inference


A classic problem in understanding human intelligence is determining how people make inductive inferences when presented with small amounts of data. We examine this question in the context of the guess-the-next-number game, where players are presented with short series of numbers and asked to guess the next one in the sequence. Our approach is unique in that we use a stochastic context free grammar to model the mathematical operations that generate a given sequence. The individual probabilities in this grammar are learned by observing people play this game, and thereby, they capture some of the mathematical inductive bias of our sample population. We then use this framework to solve novel sequence guessing problems computationally, mirroring human performance. Our goal is to better understand how people approach math problems by examining the space of mathematical functions they find easiest to both generate and recognize. We are also interested in tracking how this changes over time as functions of education and age. Finally, we examine how our results confirm a large body of psychological observations about how people approach mathematics problems.

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