We characterize the ability of human observers to learn bimodal distributions over the orientation of sequentially presented sinusoidal gratings. We focus on two distributions with modes that are either slightly overlapping or distinct. We use a recently developed technique to teach observers these distributions, and then have them produce samples from their learned distributions [1]. We demonstrate that observers can learn the distinct bimodal distribution after only 60 training samples. For the same number of samples from the overlapping bimodal, observers instead learn a unimodal distribution, typically centered between the two modes. However, with additional training, the learned distribution tends to approach the true one.

We then provide an example of a model that exhibits this behavior. The model evaluates the probability of two hypotheses: did a set of samples come from a unimodal or bimodal distribution? Evaluating the probability of each hypothesis requires integrating over the model parameters associated with that hypothesis. In a Bayesian setting, this integration naturally penalizes more complicated hypotheses - a form of Occam's razor [2]. We use the model to select the best hypothesis given samples from a bimodal distribution, varying the separation between modes and the number of training samples. The model qualitatively predicts our observers' behavior. This result suggests that humans use Occam's razor to regularize the distribution learning problem when data are insufficient. Our findings may help constrain the strategies neural systems use to learn distributions to perform inference.

[1] Sanborn, AN, Griffiths, TL. Markov chain Monte Carlo with people. NIPS, 2008.
[2] MacKay, D. Information Theory, Inference, and Learning Algorithms. 2001.