The ability to flexibly learn the structure of one’s surroundings (structure learning) is crucial foradaptive behaviour. Use of an inaccurate model of the environment can lead to incorrect inferences,and thus maladaptive actions. Despite this, relatively little is understood about how structure learningoccurs in human cognition. As a first step towards addressing this, we built on existing approaches tocreate an online clustering algorithm, in which we included a working memory component, allowingbelief update about past stimuli (retrospective inference) in contrast with the more widespread fullyonline approach. We used this model to simulate behaviour on a novel structure learning task, whereoptimal performance required estimating the number and properties of discrete clusters of continuousstimuli. In this work we show how our algorithm outperforms a parametric one (i.e. with fixednumber of clusters). We further demonstrate how retrospective inference benefits structure learning,with performance increasing with working memory capacity. We finally discuss trial-by trial measuresthat can be derived from our model, which provide testable predictions for future empirical studies.

Learning about the statistics of one’s environment is a fundamental requirement of adaptive behaviour. In this experiment we probe whether pupil dilation in response to brief auditory stimuli reflects automatic statistical learning about the underlying stimulus distributions. Specifically, we consider whether pupil dilation reflects automatic (task-irrelevant) learning about the precision of Gaussian distributions of pitch in a sequence of tones. We provide clear evidence, both by comparing responses to perceptually identical probe tones in low and high precision blocks, and using a novel model-based analysis, that subjects did indeed track the precision of the stimulus distribution. This extends previous work looking at electrophysiological effects of precision (or, equivalently, variance) learning, and provides new evidence that the putatively noradrenergic processes underlying pupil dilation reflect rapidly updated information about distributions of sensory stimuli. In addition, our study represents a validation of our model-based approach to analysing pupillometry data, which we believe has considerable promise for future studies.