Discrete Information Dynamics with Confidence via the Computational Mechanics Bootstrap: Confidence Sets and Significance Tests for Information-Dynamic Measures.

David Darmon

doi:10.3390/e22070782

Abstract

Information dynamics and computational mechanics provide a suite of measures for assessing the information- and computation-theoretic properties of complex systems in the absence of mechanistic models. However, both approaches lack a core set of inferential tools needed to make them more broadly useful for analyzing real-world systems, namely reliable methods for constructing confidence sets and hypothesis tests for their underlying measures. We develop the computational mechanics bootstrap, a bootstrap method for constructing confidence sets and significance tests for information-dynamic measures via confidence distributions using estimates of -machines inferred via the Causal State Splitting Reconstruction (CSSR) algorithm. Via Monte Carlo simulation, we compare the inferential properties of the computational mechanics bootstrap to a Markov model bootstrap. The computational mechanics bootstrap is shown to have desirable inferential properties for a collection of model systems and generally outperforms the Markov model bootstrap. Finally, we perform an in silico experiment to assess the computational mechanics bootstrap’s performance on a corpus of -machines derived from the activity patterns of fifteen-thousand Twitter users.

Highlights

Outside of the physical sciences, much of the scientific process involves model building from empirical observations
We develop the computational mechanics bootstrap, which constructs confidence distributions from time series bootstrapped from an inferred e-machine
We develop a method for bootstrapping confidence distributions for informationdynamic measures from an inferred e-machine

Summary

Introduction

Outside of the physical sciences, much of the scientific process involves model building from empirical observations. Computational mechanics subsumes information dynamics and reveals the complete computational structure of the system via its e-machine representation Together, these two approaches comprise a toolbox for analyzing time series viewed as realizations of stochastic processes, and they have been applied to physical [1,2,3], biological [4,5,6], social [7,8,9], and engineered/artificial systems [10,11,12,13]. More work must be done to move from summarizing the properties of an available time series to making inferences about the underlying process that generated the time series This is the move from descriptive statistics, which are fairly well-developed for information dynamics, to statistical inference. The three main tasks of statistical inference are point estimation, Entropy 2020, 22, 782; doi:10.3390/e22070782 www.mdpi.com/journal/entropy

Methods

Results

Discussion

Conclusion