1. Most of the human function learning literature has used tasks in which people never visualize data or functions. This is also the case in naturalistic settings where function learning takes place, where we have to form a continuous mapping between variables from experience. All of the tasks that were used in this paper involved presenting people with data in the form of a scatterplot or functional relationship, and asking them to evaluate lines applied to those axes. This task is more akin to data analysis than the traditional function learning task, and much less naturalistic. This distinction matters because performance in the two tasks is likely to be quite different. In the standard function learning task, it is quite hard to get people to learn periodic functions without other cues to periodicity. Many of the effects in this paper seem to be driven by periodic functions, suggesting that they may not hold if traditional tasks were used. I don't think this is a major problem if it is clearly acknowledged and it is made clear that the goal is to evaluate whether data-analysis systems using compositional functions match human intuitions about data analysis. But it is important if the paper is intended to be primarily about function learning in relation to the psychological literature, which has focused on a very different task. 2. I'm curious to what extent the results are due to being able to capture periodicity, rather than compositionality more generally. The comparison model is one that cannot capture periodic relationships, and in all of the experiments except Experiment 1b the relationships that people were learning involved periodicity. Would adding periodicity to the spectral kernel be enough to allow it to capture all of these results at a similar level to the explicitly compositional model? 3. Some of the details of the models are missing. In particular the grammar over kernels is not explained in any detail, making it hard to understand how this approach is applied in practice. Presumably there are also probabilities associated with the grammar that define a hypothesis space of kernels? How is inference performed?
2. I'm curious to what extent the results are due to being able to capture periodicity, rather than compositionality more generally. The comparison model is one that cannot capture periodic relationships, and in all of the experiments except Experiment 1b the relationships that people were learning involved periodicity. Would adding periodicity to the spectral kernel be enough to allow it to capture all of these results at a similar level to the explicitly compositional model?