Graphical Granger Algorithm
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A Graphical Granger Algorithm is a Time Series Analysis Algorithm that can solve a ....
- AKA: Graphical Granger Method.
- Context:
- …
- Example(s):
- an Exhaustive Granger Algorithm that tests all possible Univariate Granger Models independently
- a Lasso Granger Algorithm that uses L1-Normed Regression to choose sparse Multivariate Regression Models (Meinshausen & Buhlmann, 2006).
- a SIN Granger Algorithm that uses Matrix Inversion to find Correlations between Features across Time (Drton & Perlman, 2004).
- a Vector Auto-Regression (VAR) that fits data to Linear-Normal Time Series Model, (Gilbert, 1995)
- See: Time Series Analysis Algorithm, Cointegration.
References
2010
- (Shojaie & Michailidis, 2010) ⇒ Ali Shojaie, and George Michailidis. (2010). "Discovering graphical Granger causality using the truncating lasso penalty.". Bioinformatics, 26(18).
- ABSTRACT: Motivation: Components of biological systems interact with each other in order to carry out vital cell functions. Such information can be used to improve estimation and inference, and to obtain better insights into the underlying cellular mechanisms. Discovering regulatory interactions among genes is therefore an important problem in systems biology. Whole-genome expression data over time provides an opportunity to determine how the expression levels of genes are affected by changes in transcription levels of other genes, and can therefore be used to discover regulatory interactions among genes.
Results: In this article, we propose a novel penalization method, called truncating lasso, for estimation of causal relationships from time-course gene expression data. The proposed penalty can correctly determine the order of the underlying time series, and improves the performance of the lasso-type estimators. Moreover, the resulting estimate provides information on the time lag between activation of transcription factors and their effects on regulated genes. We provide an efficient algorithm for estimation of model parameters, and show that the proposed method can consistently discover causal relationships in the large p, small n setting. The performance of the proposed model is evaluated favorably in simulated, as well as real, data examples.
- ABSTRACT: Motivation: Components of biological systems interact with each other in order to carry out vital cell functions. Such information can be used to improve estimation and inference, and to obtain better insights into the underlying cellular mechanisms. Discovering regulatory interactions among genes is therefore an important problem in systems biology. Whole-genome expression data over time provides an opportunity to determine how the expression levels of genes are affected by changes in transcription levels of other genes, and can therefore be used to discover regulatory interactions among genes.
2009
- (Lozano et al., 2009) ⇒ Aurelie C. Lozano, Naoki Abe, Yan Liu, and Saharon Rosset. (2009). “Grouped Graphical Granger Modeling Methods for Temporal Causal Modeling.” In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD-2009). doi:10.1145/1557019.1557085
- ABSTRACT : We develop and evaluate an approach to causal modeling based on time series data, collectively referred to as “grouped graphical Granger modeling methods." Graphical Granger modeling uses graphical modeling techniques on time series data and invokes the notion of “Granger causality” to make assertions on causality among a potentially large number of time series variables through inference on time-lagged effects. The present paper proposes a novel enhancement to the graphical Granger methodology by developing and applying families of regression methods that are sensitive to group information among variables, to leverage the group structure present in the lagged temporal variables according to the time series they belong to. Additionally, we propose a new family of algorithms we call group boosting, as an improved component of grouped graphical Granger modeling over the existing regression methods with grouped variable selection in the literature (e.g group Lasso). The introduction of group boosting methods is primarily motivated by the need to deal with non-linearity in the data. We perform empirical evaluation to confirm the advantage of the grouped graphical Granger methods over the standard (non-grouped) methods, as well as that specific to the methods based on group boosting. This advantage is also demonstrated for the real world application of gene regulatory network discovery from time-course microarray data.
2007
- (Arnold et al., 2007) ⇒ Andrew Arnold, Yan Liu, and Naoki Abe (2007). “Temporal Causal Modeling with Graphical Granger Methods.” In: Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD-2007).