Memory Order Decomposition of Symbolic Sequences

Abstract

We introduce a general method for the study of memory in symbolic sequences based on higher-order Markov analysis. The Markov process that best represents a sequence is expressed as a mixture of matrices of minimal orders, enabling the definition of the so-called memory profile, which unambiguously reflects the true order of correlations. The method is validated by recovering the memory profiles of tunable synthetic sequences. Finally, we scan real data and showcase with practical examples how our protocol can be used to extract relevant stochastic properties of symbolic sequences.

arXiv comment7 pages, 2 figures

References in corpus (10)

• Power laws, Pareto distributions and Zipf's law
• Temporal Networks
• Memory in network flows and its effects on spreading dynamics and community detection
• Causality-Driven Slow-Down and Speed-Up of Diffusion in Non-Markovian Temporal Networks
• Betweenness Preference: Quantifying Correlations in the Topological Dynamics of Temporal Networks
• Networks of motifs from sequences of symbols
• A non extensive approach to the entropy of symbolic sequences
• Effects of memory on spreading processes in non-Markovian temporal networks
• Multiplex decomposition of non-Markovian dynamics and the hidden layer reconstruction problem
• Decomposition of conditional probability for high-order symbolic Markov chains