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Dynamical Structure Function and Granger Causality: Similarities and differences

Yue, Zuogong ; Thunberg, Johan LU ; Yuan, Ye and Goncalves, Jorge (2015) 54th IEEE Conference on Decision and Control, CDC 2015 p.889-894
Abstract
Causal networks are essential in many applications to illustrate causal relations in dynamical systems. In a view of statistics, Granger Causality (GC) gives a definition for causal ordering of time series, which implies a parametric model for stationary processes. In a systematic view, Dynamical Structure Function (DSF) is proposed to provide a general parametric representation for linear causal networks based on state space representations. It is difficult to determine which definition should be adopted for a particular application. By introducing an intermediate form of DSF, this article connects GC for stationary processes with DSF. Both GC and DSF essentially represent the same notion of causality but with important differences with... (More)
Causal networks are essential in many applications to illustrate causal relations in dynamical systems. In a view of statistics, Granger Causality (GC) gives a definition for causal ordering of time series, which implies a parametric model for stationary processes. In a systematic view, Dynamical Structure Function (DSF) is proposed to provide a general parametric representation for linear causal networks based on state space representations. It is difficult to determine which definition should be adopted for a particular application. By introducing an intermediate form of DSF, this article connects GC for stationary processes with DSF. Both GC and DSF essentially represent the same notion of causality but with important differences with respect to how they encode latent variables. This article also addresses the relations between graphs defined by GC and DSF. Furthermore, the uniqueness of parametric representations is addressed, which is essential in network inference. Results from different fields are surveyed and categorized into two categories - networks with exogeneity and networks without exogeneity. Limitations on sufficient conditions to guarantee exact identification are discussed under different assumptions on systems. In the end, a figure is used to summarize the relationships between various representations of causal dynamical networks and their identifiability conditions in LTI systems. (Less)
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author
; ; and
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
2015 54th IEEE Conference on Decision and Control (CDC)
pages
889 - 894
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
54th IEEE Conference on Decision and Control, CDC 2015
conference location
Osaka, Japan
conference dates
2015-12-15 - 2015-12-18
external identifiers
  • scopus:84962030088
ISBN
978-1-4799-7886-1
DOI
10.1109/CDC.2015.7402341
language
English
LU publication?
no
id
890bd6f8-84f1-4dbc-bc25-148050e64757
date added to LUP
2024-09-05 14:37:19
date last changed
2024-09-23 12:02:29
@inproceedings{890bd6f8-84f1-4dbc-bc25-148050e64757,
  abstract     = {{Causal networks are essential in many applications to illustrate causal relations in dynamical systems. In a view of statistics, Granger Causality (GC) gives a definition for causal ordering of time series, which implies a parametric model for stationary processes. In a systematic view, Dynamical Structure Function (DSF) is proposed to provide a general parametric representation for linear causal networks based on state space representations. It is difficult to determine which definition should be adopted for a particular application. By introducing an intermediate form of DSF, this article connects GC for stationary processes with DSF. Both GC and DSF essentially represent the same notion of causality but with important differences with respect to how they encode latent variables. This article also addresses the relations between graphs defined by GC and DSF. Furthermore, the uniqueness of parametric representations is addressed, which is essential in network inference. Results from different fields are surveyed and categorized into two categories - networks with exogeneity and networks without exogeneity. Limitations on sufficient conditions to guarantee exact identification are discussed under different assumptions on systems. In the end, a figure is used to summarize the relationships between various representations of causal dynamical networks and their identifiability conditions in LTI systems.}},
  author       = {{Yue, Zuogong and Thunberg, Johan and Yuan, Ye and Goncalves, Jorge}},
  booktitle    = {{2015 54th IEEE Conference on Decision and Control (CDC)}},
  isbn         = {{978-1-4799-7886-1}},
  language     = {{eng}},
  pages        = {{889--894}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Dynamical Structure Function and Granger Causality: Similarities and differences}},
  url          = {{http://dx.doi.org/10.1109/CDC.2015.7402341}},
  doi          = {{10.1109/CDC.2015.7402341}},
  year         = {{2015}},
}