Graphical modelling of multivariate time series

Eichler, Michael

doi:10.1007/s00440-011-0345-8

Cited by 145 publications

(165 citation statements)

References 39 publications

(82 reference statements)

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“…The remarkable success of Granger causality via the VAR approach in different applications [3,4,12,18,21] has led to definition of Granger Graphical models [5,7] and Directed Information Graphs [23]. Both graphical models are obtained via graphical representation of each time series with a node and the dependency of the future of a time series X i (t) to past values of another time series X j (t) via a directed edge X j → X i in the graph.…”

Section: Preliminaries and Related Workmentioning

confidence: 99%

“…Several key steps have been taken by Eichler in analysis of effects of unobserved confounders in Granger graphical models, see [7] and the references therein. He introduced the m-separation criteria, as the counterpart of Pearl's d-separation in causal graphs [22], for detection of connectivity of spurious paths in Granger graphs using causal priors on the unobserved time series.…”

Section: Preliminaries and Related Workmentioning

confidence: 99%

“…In attempt to cancel out the effects of unobserved confounders, authors in [6,7,8] have extended Pearl's criteria [22] for determining a set of time series that via conditioning on them the spurious causation paths are blocked and the Granger causality identifies the true temporal dependency graph. As shown in Fig 1, by analysis of the effects of unobserved confounders in simple structures, Figure 1: The sequence of the theoretical results: Theorem 3.1 utilizes path delays to find a subset of time series that via conditioning on them we are able to cancel out the spurious confounder effects.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Examination of Practical Granger Causality Inference

Liu

Bahadori

2013

Proceedings of the 2013 SIAM International Conference on Data Mining

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Learning temporal causal structures among multiple time series is one of the major tasks in mining time series data. Granger causality is one of the most popular techniques in uncovering the temporal dependencies among time series; however it faces two main challenges: (i) the spurious effect of unobserved time series and (ii) the computational challenges in high dimensional settings. In this paper, we utilize the confounder path delays to find a subset of time series that via conditioning on them we are able to cancel out the spurious confounder effects. After study of consistency of different Granger causality techniques, we propose Copula-Granger and show that while it is consistent in high dimensions, it can efficiently capture non-linearity in the data. Extensive experiments on a synthetic and a social networking dataset confirm our theoretical results. IntroductionIn the era of data deluge, we are confronted with largescale time series data, i.e., a sequence observations of concerned variables over a period of time. For example, terabytes of neural activity time series data are produced to record the collective response of neurons to different stimuli; petabytes of climate and meteorological data, such as temperature, solar radiation, and precipitation, are collected over the years; and exabytes of social media contents are generated over time on the Internet. A major data mining task for time series data is to uncover the temporal causal relationship among the time series. For example, in the climatology, we want to identify the factors that impact the climate patterns of certain regions. In social networks, we are interested in identification of the patterns of influence among users and how topics activate or suppress each other. Developing effective and scalable data mining algorithms to uncover temporal dependency structures between time series and reveal insights from data has become a key problem in machine learning and data mining.There are two major challenges in discovering temporal causal relationship in large-scale data: (i) not all influential confounders are observed in the datasets and

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Section: Preliminaries and Related Workmentioning

confidence: 99%

Section: Preliminaries and Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Examination of Practical Granger Causality Inference

Liu

Bahadori

2013

Proceedings of the 2013 SIAM International Conference on Data Mining

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“…This was originally studied in the setting when the variables are jointly Gaussian and hence the dependence is linear (see [6] for the original treatment, and [7,8] for versions with latent variables). This problem was generalized to the setting with arbitrary probability distributions and temporal dependences in [9] and studied further in [10], for one-step markov chains in [11] and deterministic relationships in [12]. From these works, under some technical condition, we can assert that the following method is guaranteed to be consistent,…”

Section: Introductionmentioning

confidence: 99%

Potential conditional mutual information: Estimators and properties

Rahimzamani

Kannan

2017

Preprint

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The conditional mutual information I(X; Y |Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model inference, causal strength estimation and time-series problems. In several applications, it is desirable to have a functional purely of the conditional distribution p Y |X,Z rather than of the joint distribution pX,Y,Z . We define the potential conditional mutual information as the conditional mutual information calculated with a modified joint distribution p Y |X,Z qX,Z , where qX,Z is a potential distribution, fixed airport. We develop K nearest neighbor based estimators for this functional, employing importance sampling, and a coupling trick, and prove the finite k consistency of such an estimator. We demonstrate that the estimator has excellent practical performance and show an application in dynamical system inference.

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“…The derived graphical representations in this study contain vertices referring to the acquired time-series data and edges that are defined in terms of Granger causality, hence are directed. This kind of graph is then referred to as a Granger causality graph [2,24,25].…”

Section: Introductionmentioning

confidence: 99%

The impact of latent confounders in directed network analysis in neuroscience

Ramb

Eichler

Ing

et al. 2013

Phil. Trans. R. Soc. A.

Self Cite

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In the analysis of neuroscience data, the identification of task-related causal relationships between various areas of the brain gives insights about the network of physiological pathways that are active during the task. One increasingly used approach to identify causal connectivity uses the concept of Granger causality that exploits predictability of activity in one region by past activity in other regions of the brain. Owing to the complexity of the data, selecting components for the analysis of causality as a preprocessing step has to be performed. This includes predetermined—and often arbitrary—exclusion of information. Therefore, the system is confounded by latent sources. In this paper, the effect of latent confounders is demonstrated, and paths of influence among three components are studied. While methods for analysing Granger causality are commonly based on linear vector autoregressive models, the effects of latent confounders are expected to be present also in nonlinear systems. Therefore, all analyses are also performed for a simulated nonlinear system and discussed with regard to applications in neuroscience.

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Graphical modelling of multivariate time series

Cited by 145 publications

References 39 publications

An Examination of Practical Granger Causality Inference

An Examination of Practical Granger Causality Inference

Potential conditional mutual information: Estimators and properties

The impact of latent confounders in directed network analysis in neuroscience

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