Learning Temporal Structures of Random Patterns
This work provides a mathematical framework for analyzing temporal patterns in stochastic processes, which could benefit researchers in cognitive science and machine learning, though it appears incremental as it builds on existing statistical methods.
The paper tackles the problem of extracting temporal regularities from random sequences by presenting a method using generating functions to compute pattern time statistics for Markov and Bernoulli trials, showing that these statistics cover a wide range of measurements used in human and machine learning studies.
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.