Partial Autoinformation to Characterize Symbolic Sequences.

Area of Science:

• Information Theory
• Statistical Physics
• Time Series Analysis
• Computational Neuroscience

Background:

• Discrete stochastic processes are fundamental in modeling complex systems.
• Determining the Markov order is crucial for understanding temporal dependencies.
• Existing methods for metric time series are not directly applicable to symbolic data.

Purpose of the Study:

• To introduce novel information-theoretic measures for numerically determining the Markov order of discrete stochastic processes.
• To quantify statistical dependencies in symbolic time series using Shannon entropy.
• To analyze temporal structures in various theoretical and experimental data sets.

Main Methods:

• Development of autoinformation (time-lagged mutual information) to measure dependencies between time points.
• Development of partial autoinformation (conditional mutual information) to account for intermediate values.
• Application of these measures to theoretical Markov/non-Markov processes, statistical physics models, and EEG data.

Main Results:

• Autoinformation and partial autoinformation successfully reveal temporal structures in diverse data.
• Partial autoinformation accurately identifies the Markov order and detects non-Markovian effects.
• The methods correctly identified the underlying Markov order in hidden Markov models (HMMs).

Conclusions:

• The proposed information-theoretic measures provide powerful tools for analyzing symbolic time series.
• These methods can be used as an initial step to discover higher-order Markov dependencies and non-Markovianity.
• The approach is applicable to experimental, non-metric time series analysis, including periodicities.