An Information Criterion for Inferring Coupling of Distributed Dynamical Systems

Abstract

The behavior of many real-world phenomena can be modeled by non-linear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of coupled maps as a synchronous update graph dynamical system. Specifically, we study the structure learning problem for spatially distributed dynamical systems coupled via a directed acyclic graph. Unlike established structure learning procedures that find locally maximum posterior probabilities of a network structure containing latent variables, our work exploits the properties of dynamical systems to compute globally optimal approximations of these distributions. We arrive at this result by the use of time delay embedding theorems. Taking an information-theoretic perspective, we show that the log-likelihood has an intuitive interpretation in terms of information transfer.

RoboCup 2D Soccer Simulation League: Evaluation Challenges

“…Tracing such advances is especially important because different champion teams usually employ different approaches, often achieving a high degree of specialisation in a sub-field of AI, for example, automated hierarchical planning developed by WrightEagle [23,24,26,21,28], opponent modelling studied by HELIOS [27], and human-based evolutionary computation adopted by Gliders [11,12]. Many more research areas are likely to contribute towards improving the League, and several general research directions are recognised as particularly promising: nature-inspired collective intelligence [29,30,31], embodied intelligence [32,33,34,35], information theory of distributed cognitive systems [36,37,38,39,40,41], guided self-organisation [42,43,44], and deep learning [45,46,47].…”

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“…Directed information-theoretic measures, such as transfer entropy [39], are particularly suited to this task in real systems in either the time-averaged or local forms [40]. These quantities have been used previously to infer interaction networks in multi-agent systems [41] and are particularly suited to processes with attracting states [42,43]. This would allow us to study contact networks in terms of both structural and functional connectivity [44,45,46,47] and their dominant motifs [48,49,50].…”

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“…Although the algorithms presented in these papers can infer driving subsystems in a spatially distributed dynamical system, the results obtained differ from ours as inference is not considered for an entire network structure, nor is a formal derivation presented. Contrasting this, we recently derived an information criterion for learning the structure of distributed dynamical systems [ 12 ]. However, the criterion proposed required parametric modelling of the probability distributions, and thus a detailed understanding of the physical phenomena being studied.…”

“…We represent such a spatially distributed system as a probabilistic graphical model termed a synchronous graph dynamical system (GDS) [ 11 , 12 ], whose structure is given by a DAG. Model selection in this context is the problem of inferring directed relationships between hidden variables from an observed dataset, also known as structure learning .…”