Abstract
Inferring the coupling structure of complex systems from time series data in general by means of statistical and information-theoretic techniques is a challenging problem in applied science. The reliability of statistical inferences requires the construction of suitable information-theoretic measures that take into account both direct and indirect influences, manifest in the form of information flows, between the components within the system. In this work, we present an application of the optimal causation entropy (oCSE) principle to identify the coupling structure of a synthetic biological system, the repressilator. Specifically, when the system reaches an equilibrium state, we use a stochastic perturbation approach to extract time series data that approximate a linear stochastic process. Then, we present and jointly apply the aggregative discovery and progressive removal algorithms based on the oCSE principle to infer the coupling structure of the system from the measured data. Finally, we show that the success rate of our coupling inferences not only improves with the amount of available data, but it also increases with a higher frequency of sampling and is especially immune to false positives.
Highlights
Deducing equations of dynamics from empirical observations is fundamental in science
We considered the challenging problem of inferring the causal structure of complex systems from limited available data
We presented an application of the so-called optimal causation entropy (oCSE) principle to identify the coupling structure of a synthetic biological system, the repressilator
Summary
Deducing equations of dynamics from empirical observations is fundamental in science. The laws of celestial mechanics were deduced based on observations of planet trajectories [1]; the forms of chemical equations were inferred upon empirical reaction relations and kinetics [2]; the principles of economics were uncovered through market data analysis [3]. Despite such important accomplishments, the general problem of identifying dynamical equations from data is a challenging one. The classical Granger causality is limited to coupled linear systems, while most recently developed methods based on information-theoretic measures are applicable to virtually any model, their effectiveness relies on the abundance of data. The Causality Quiz: answer “Yes” or “No” to the following questions, and explain why
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