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Causation entropy from symbolic representations of dynamical systems
Carlo Cafaro1, Warren M Lord1, Jie Sun1
1Department of Mathematics, Clarkson University, 8 Clarkson Ave, Potsdam, New York, 13699-5815, USA.
Chaos (Woodbury, N.Y.)
|May 3, 2015
Summary
Symbolization of complex system data affects causal structure and Markov order. These key properties depend sensitively and nonmonotonically on symbolization choices, deviating from analog counterparts.
Area of Science:
- Complex Systems Analysis
- Information Theory
- Dynamical Systems
Background:
- Identifying causal structures and information flow in complex systems is crucial for many applications.
- Data from dynamical processes are often symbolized due to measurement limitations or statistical needs.
Purpose of the Study:
- To investigate the impact of data symbolization on causal structure and Markov order.
- To analyze the effects of symbolization on information flow quantification in complex systems.
Main Methods:
- Algorithmic application of causation entropy.
- Analysis of the tent map as a model complex system.
- Investigation of symbolization's effect on Markov order and causal structure.
Main Results:
- Symbolization significantly and nonmonotonically impacts Markov order and causal structure.
- These properties are highly sensitive to the specific symbolization method chosen.
- Markov order and causal structure may not converge to analog values with finer partitioning.
Conclusions:
- Symbolization is a critical factor that can distort the inferred causal relationships and information flow in complex systems.
- Careful consideration of symbolization is necessary when analyzing dynamical systems data.
- The choice of symbolization method directly influences the reliability of derived causal insights.
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