PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Detecting the Direction of Causal Time Series
Jonas Peters, Dominik Janzing, Arthur Gretton and Bernhard Schölkopf
The 26th International Conference on Machine Learning (ICML 2009) pp. 801-808, 2009.


We propose a method that detects the true direction of time series, by fitting an autoregressive moving average model to the data. Whenever the noise is independent of the previous samples for one ordering of the observations, but dependent for the opposite ordering, we infer the former direction to be the true one. We prove that our method works in the population case as long as the noise of the process is not normally distributed (for the latter case, the direction is not identifiable). A new and important implication of our result is that it confirms a fundamental conjecture in causal reasoning --- if after regression the noise is independent of signal for one direction and dependent for the other, then the former represents the true causal direction --- in the case of time series. We test our approach on two types of data: simulated data sets conforming to our modeling assumptions, and real world EEG time series. Our method makes a decision for a significant fraction of both data sets, and these decisions are mostly correct. For real world data, our approach outperforms alternative solutions to the problem of time direction recovery.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:7811
Deposited By:Jonas Peters
Deposited On:17 March 2011