Data Availability and Function Extrapolation

In function learning experiments, where participants learn relationships from sequentially-presented examples, people show a strong tacit expectation that most relationships are linear, and struggle to learn and extrapolate from non-linear relationships. In contrast, experiments with similar tasks where data are presented simultaneously – typically using scatter plots – have shown that human learners can discover and extrapolate from complex non-linear trends. Do people have different expectations in these task types, or can the results be attributed to effects of memory and data availability? In a direct comparison of both paradigms, we found that differences between task types can be attributed to data availability. We show that a simple memory-limited Bayesian model is consistent with human extrapolations for linear data for both high and low data availability. However, our model underestimates the participants’ ability to infer non-monotonic functions, especially when data is sparse. This suggest that people track higher-order properties of functions when learning and generalizing.
Keywords: function learning, function estimation, resource rationality