# Learning from Games: Inductive Bias and Bayesian Inference

- Michael Coen,
*University of Wisconsin-Madison*
- Yue Gao,
*University of Wisconsin-Madison*

## Abstract

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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