Dynamical Structure Function and Granger Causality: Similarities and differences

Yue, Zuogong; Thunberg, Johan; Yuan, Ye

doi:10.1109/cdc.2015.7402341

Cited by 3 publications

(1 citation statement)

References 31 publications

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“…Linear dynamic graphs consider models of the form [10], [12]: Closely related to the notion of linear dynamical graphs is the dynamical structure function (DSF) [3], [27], [5], [28], [29]. Although defined for linear systems like LDGs, the DSF differs from LDGs, DIGs, and MGMs in that it is not developed in the stochastic setting and considers inputs that may-or-may-not be stochastic in nature.…”

Section: Signal Structure Of a Systemmentioning

confidence: 99%

Shared hidden state and network representations of interconnected dynamical systems

Warnick

2015

2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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This paper demonstrates that the signal structure of an interconnected dynamical system, such as that represented by various dynamical graphical models, can be very different from the interconnection structure of its subsystems. These differences are revealed by considering the network semantics of each representation, characterized by the set of realizations consistent with each network structure. The reason these system networks can be so different is that subsystems never share hidden state, and thus subsystem structures partition the entire system state, while signal structures remain agnostic towards the presence of shared hidden state. Remaining agnostic towards the presence of shared hidden state make signal structures a weaker description of the underlying system structure, but it also gives signal structures a lower information cost for identification. Identifying a system's subsystem structure demands the identification of the correct partition of system states, which can be very expensive.

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Section: Signal Structure Of a Systemmentioning

confidence: 99%

Shared hidden state and network representations of interconnected dynamical systems

Warnick

2015

2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Causality based graph structure of stochastic linear state-space representations

Jozsa

Petreczky

Camlibel

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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Relationship Between Granger Noncausality and Network Graph of State-Space Representations

Jozsa

Petreczky

Camlibel

2019

IEEE Trans. Automat. Contr.

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1 the network structure is to understand when the observed behaviour could, in principle, be realized by a state-space representation with a specific network structure. The same holds for structure preserving model reduction: it is useful to know whether a minimal (in terms of the dimension of states) realization admitting a specific network structure is for a certain behaviour. For the design of interconnected systems, understanding the relationship between the observed behaviour and the network structure could open up the possibility of choosing alternative network structures realizing the same functionality. The motivation for studying coordinated linear systems is that their network structure is a simple but natural one, occurring in many applications [19].The need to understand the relationship between the observed behaviour and the network structure of linear systems is an active research area, see for example [22,23,17]. However, none of the cited work addressed linear stochastic systems. Causality relationship between time series is an established research topic in econometrics, neuroscience and control theory. This relationship can be characterized in terms of the network structure of input-output representations of these processes, see [7,11,10,2,8] and the references therein. If there is one agent, then our results can be viewed as a counterparts of the cited papers for state-space representations. In fact, for n = 2 Granger causality for state-space representation was studied by using transfer function approach [16]. In contrast with the results in [16] we give a state-space characterization for Granger non-causality by constructing it, by choosing a state process for which the system matrices are in specific form. The papers [5,6,4] are the closest ones to this paper, they provide necessary and sufficient conditions for the existence of a linear state-space realization in the so called conditional orthogonal form. Conditionally orthogonal state-space realizations represent a specific subclass of coordinated linear stochastic systems, and the conditions for the existence of such a system are much stronger than the conditions proposed in this paper. Note that [5,6,4] presented conditions for existence of conditionally orthogonal state-space representations, but in contrast to this paper, [5, 6, 4] did not address their minimality.Coordinated linear systems for deterministic case were studied in [15,14,19]. In [15, 14] a general method was presented to transform a system into coordinated form. In [18,14] also Gaussian coordinated systems were studied and their LQG control. In this paper we deal with linear stochastic systems (not necessarily Gaussian) and we observe the existence of a linear state-space representation in coordinated form in terms of the causal properties of the output processes.The structure of the paper is the following: in section 1 we introduce the results for n = 2, when besides the coordinator there is one agent. We state that Granger non-causality is equivalent with a Kalman repre...

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Dynamical Structure Function and Granger Causality: Similarities and differences

Cited by 3 publications

References 31 publications

Shared hidden state and network representations of interconnected dynamical systems

Shared hidden state and network representations of interconnected dynamical systems

Causality based graph structure of stochastic linear state-space representations

Relationship Between Granger Noncausality and Network Graph of State-Space Representations

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