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Abstract Data-driven analysis and monitoring of complex dynamical systems have been gaining popularity due to various reasons like ubiquitous sensing and advanced computation capabilities. A key rationale is that such systems inherently have high dimensionality and feature complex subsystem interactions due to which majority of the first-principle based methods become insufficient. We explore the family of a recently proposed probabilistic graphical modeling technique, called spatiotemporal pattern network (STPN) in order to capture the Granger causal relationships among observations in a dynamical system. We also show that this technique can be used for anomaly detection and root-cause analysis for real-life dynamical systems. In this context, we introduce the notion of Granger-STPN (G-STPN) inspired by the notion of Granger causality and introduce a new nonparametric technique to detect causality among dynamical systems observations. We experimentally validate our framework for detecting anomalies and analyzing root causes in a robotic arm platform and obtain superior results compared to when other causality metrics were used in previous frameworks.
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Non-Asymptotic Guarantees for Reliable Identification of Granger Causality via the LASSO
Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this methodology are: 1) over-fitting as a result of limited data duration, and 2) correlated process noise as a confounding factor, both leading to errors in identifying the causal influences. Sparse estimation via the LASSO has successfully addressed these challenges for parameter estimation. However, the classical statistical tests for Granger causality resort to asymptotic analysis of ordinary least squares, which require long data duration to be useful and are not immune to confounding effects. In this work, we address this disconnect by introducing a LASSO-based statistic and studying its non-asymptotic properties under the assumption that the true models admit sparse autoregressive representations. We establish fundamental limits for reliable identification of Granger causal influences using the proposed LASSO-based statistic. We further characterize the false positive error probability and test power of a simple thresholding rule for identifying Granger causal effects and provide two methods to set the threshold in a data-driven fashion. We present simulation studies and application to real data to compare the performance of our proposed method to ordinary least squares and existing LASSO-based methods in detecting Granger causal influences, which corroborate our theoretical results.
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- PAR ID:
- 10472331
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Transactions on Information Theory
- Volume:
- 69
- Issue:
- 11
- ISSN:
- 0018-9448
- Page Range / eLocation ID:
- 7439 to 7460
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TIT.2023.3296336
