Abstract
Complex systems arise as a result of the nonlinear interactions between components. In particular, the evolutionary dynamics of a multivariate system encodes the ways in which different variables interact with each other individually or in groups. One fundamental question that remains unanswered is: How do two non-overlapping multivariate subsets of variables interact to causally determine the outcome of a specific variable? Here, we provide an information-based approach to address this problem. We delineate the temporal interactions between the bundles in a probabilistic graphical model. The strength of the interactions, captured by partial information decomposition, then exposes complex behavior of dependencies and memory within the system. The proposed approach successfully illustrated complex dependence between cations and anions as determinants of pH in an observed stream chemistry system. In the studied catchment, the dynamics of pH is a result of both cations and anions through mainly synergistic effects of the two and their individual influences as well. This example demonstrates the potentially broad applicability of the approach, establishing the foundation to study the interaction between groups of variables in a range of complex systems.
Highlights
In complex systems shaped by the interaction of a multitude of variables, an interesting question that remains unanswered is: In what ways do the evolutionary history of two subsets of variables interactively influence the current state of a target variable? Answering this question would be extremely useful in furthering our understanding in the collective behavior of a system’s dynamics, where the interactions of variables in groups play a key role
We present an information flow-based framework to characterize the joint influence from the evolutionary dynamics of two groups of variables on the present state of a target variable
Partitioning the total information into synergistic, redundant, and unique components helps delineate different information characteristics due to the two bundled sets. This framework was applied to observed stream chemistry datasets, and successfully showed the joint impacts of cations and anions on stream pH
Summary
In complex systems shaped by the interaction of a multitude of variables, an interesting question that remains unanswered is: In what ways do the evolutionary history of two subsets of variables interactively influence the current state of a target variable? Answering this question would be extremely useful in furthering our understanding in the collective behavior of a system’s dynamics, where the interactions of variables in groups play a key role. We propose new information measures to quantify and characterize the interactive strength among two bundled variable sets in affecting the present state of a target variable (Figure 1c) This approach allows us: (1) to consider the effect of the entire evolutionary history of all interacting variables, termed causal history [9,10], that determines the current state of a variable of interest; and (2) to characterize such effect by using partial information decomposition (PID) [11] framework. This approach is called momentary partial information decomposition, building on the idea of momentary information and PID Another illustrative example of using information measures to assess multivariate interaction is the causal history analysis framework [10,12], which accounts for the influence from the entire evolutionary dynamics of the system (Figure 1c).
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