# A rational model of function learning

- Christopher Lucas,
*UC Berkeley*
- Thomas Griffiths,
*UC Berkeley*
- Michael Kalish,
*University of Lafayette*

## Abstract

People often face the problem of learning what value a variable
will take, given information about the values of other variables. Categorization
and causal prediction are special cases, each the subject of extensive research
dealing exclusively with discrete variables. With continuous variables, this
problem is known as function learning. Most function learning research has been
concerned with specifying representations and processes by which people
understand the functional relationship between pairs of continuous variables. In
contrast, we present a rational model that transparently identifies the inductive
biases that a process model should seek to capture. The foundation of our
approach is an infinite mixture of Gaussian process experts. It extends our
previous Gaussian process model, which outperforms several well-known
alternatives and has been shown to be a generalization of both associative and
rule-based (i.e., regression-like) function-learning models. We find that it
explains several phenomena, including knowledge partitioning and iterated
learning data.

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