Learning Temporal Structures of Random Patterns

A cornerstone of human statistical learning is the ability to extract temporal regularities / patterns from random sequences. Here we present a method of computing pattern time statistics with generating functions for first-order Markov trials and independent Bernoulli trials. We show that the pattern time statistics cover a wide range of measurements commonly used in existing studies of both human and machine learning of stochastic processes, including probability of alternation, temporal correlation between pattern events, and related variance / risk measures. Moreover, we show that recurrent processing and event segmentation by pattern overlap may provide a coherent explanation for the sensitivity of the human brain to the rich statistics and the latent structures in the learning environment.