Learning Temporal Structures of Random Patterns

TL;DR

This paper introduces a method for analyzing temporal regularities in random sequences using generating functions, revealing insights into human and machine learning of stochastic patterns.

Contribution

It presents a novel approach to compute pattern time statistics for Markov and Bernoulli trials, linking statistical measures to neural processing and pattern segmentation.

Findings

Pattern time statistics encompass key measures like alternation probability and temporal correlation.

Recurrent processing and event segmentation explain human sensitivity to complex statistical structures.

The method unifies analysis of stochastic processes relevant to both human cognition and machine learning.

Abstract

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.