Discovering Temporal Causal Relations from Subsampled Data

Mingming Gong, Kun Zhang, Bernhard Schoelkopf, Dacheng Tao, Philipp Geiger
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:1898-1906, 2015.

Abstract

Granger causal analysis has been an important tool for causal analysis for time series in various fields, including neuroscience and economics, and recently it has been extended to include instantaneous effects between the time series to explain the contemporaneous dependence in the residuals. In this paper, we assume that the time series at the true causal frequency follow the vector autoregressive model. We show that when the data resolution becomes lower due to subsampling, neither the original Granger causal analysis nor the extended one is able to discover the underlying causal relations. We then aim to answer the following question: can we estimate the temporal causal relations at the right causal frequency from the subsampled data? Traditionally this suffers from the identifiability problems: under the Gaussianity assumption of the data, the solutions are generally not unique. We prove that, however, if the noise terms are non-Gaussian, the underlying model for the high frequency data is identifiable from subsampled data under mild conditions. We then propose an Expectation-Maximization (EM) approach and a variational inference approach to recover temporal causal relations from such subsampled data. Experimental results on both simulated and real data are reported to illustrate the performance of the proposed approaches.

Cite this Paper


BibTeX
@InProceedings{pmlr-v37-gongb15, title = {Discovering Temporal Causal Relations from Subsampled Data}, author = {Gong, Mingming and Zhang, Kun and Schoelkopf, Bernhard and Tao, Dacheng and Geiger, Philipp}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {1898--1906}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/gongb15.pdf}, url = { http://proceedings.mlr.press/v37/gongb15.html }, abstract = {Granger causal analysis has been an important tool for causal analysis for time series in various fields, including neuroscience and economics, and recently it has been extended to include instantaneous effects between the time series to explain the contemporaneous dependence in the residuals. In this paper, we assume that the time series at the true causal frequency follow the vector autoregressive model. We show that when the data resolution becomes lower due to subsampling, neither the original Granger causal analysis nor the extended one is able to discover the underlying causal relations. We then aim to answer the following question: can we estimate the temporal causal relations at the right causal frequency from the subsampled data? Traditionally this suffers from the identifiability problems: under the Gaussianity assumption of the data, the solutions are generally not unique. We prove that, however, if the noise terms are non-Gaussian, the underlying model for the high frequency data is identifiable from subsampled data under mild conditions. We then propose an Expectation-Maximization (EM) approach and a variational inference approach to recover temporal causal relations from such subsampled data. Experimental results on both simulated and real data are reported to illustrate the performance of the proposed approaches.} }
Endnote
%0 Conference Paper %T Discovering Temporal Causal Relations from Subsampled Data %A Mingming Gong %A Kun Zhang %A Bernhard Schoelkopf %A Dacheng Tao %A Philipp Geiger %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-gongb15 %I PMLR %P 1898--1906 %U http://proceedings.mlr.press/v37/gongb15.html %V 37 %X Granger causal analysis has been an important tool for causal analysis for time series in various fields, including neuroscience and economics, and recently it has been extended to include instantaneous effects between the time series to explain the contemporaneous dependence in the residuals. In this paper, we assume that the time series at the true causal frequency follow the vector autoregressive model. We show that when the data resolution becomes lower due to subsampling, neither the original Granger causal analysis nor the extended one is able to discover the underlying causal relations. We then aim to answer the following question: can we estimate the temporal causal relations at the right causal frequency from the subsampled data? Traditionally this suffers from the identifiability problems: under the Gaussianity assumption of the data, the solutions are generally not unique. We prove that, however, if the noise terms are non-Gaussian, the underlying model for the high frequency data is identifiable from subsampled data under mild conditions. We then propose an Expectation-Maximization (EM) approach and a variational inference approach to recover temporal causal relations from such subsampled data. Experimental results on both simulated and real data are reported to illustrate the performance of the proposed approaches.
RIS
TY - CPAPER TI - Discovering Temporal Causal Relations from Subsampled Data AU - Mingming Gong AU - Kun Zhang AU - Bernhard Schoelkopf AU - Dacheng Tao AU - Philipp Geiger BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-gongb15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 1898 EP - 1906 L1 - http://proceedings.mlr.press/v37/gongb15.pdf UR - http://proceedings.mlr.press/v37/gongb15.html AB - Granger causal analysis has been an important tool for causal analysis for time series in various fields, including neuroscience and economics, and recently it has been extended to include instantaneous effects between the time series to explain the contemporaneous dependence in the residuals. In this paper, we assume that the time series at the true causal frequency follow the vector autoregressive model. We show that when the data resolution becomes lower due to subsampling, neither the original Granger causal analysis nor the extended one is able to discover the underlying causal relations. We then aim to answer the following question: can we estimate the temporal causal relations at the right causal frequency from the subsampled data? Traditionally this suffers from the identifiability problems: under the Gaussianity assumption of the data, the solutions are generally not unique. We prove that, however, if the noise terms are non-Gaussian, the underlying model for the high frequency data is identifiable from subsampled data under mild conditions. We then propose an Expectation-Maximization (EM) approach and a variational inference approach to recover temporal causal relations from such subsampled data. Experimental results on both simulated and real data are reported to illustrate the performance of the proposed approaches. ER -
APA
Gong, M., Zhang, K., Schoelkopf, B., Tao, D. & Geiger, P.. (2015). Discovering Temporal Causal Relations from Subsampled Data. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:1898-1906 Available from http://proceedings.mlr.press/v37/gongb15.html .

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