A Kernel Independence Test for Random Processes

Kacper Chwialkowski, Arthur Gretton
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):1422-1430, 2014.

Abstract

A non-parametric approach to the problem of testing the independence of two random processes is developed. The test statistic is the Hilbert-Schmidt Independence Criterion (HSIC), which was used previously in testing independence for i.i.d. pairs of variables. The asymptotic behaviour of HSIC is established when computed from samples drawn from random processes. It is shown that earlier bootstrap procedures which worked in the i.i.d. case will fail for random processes, and an alternative consistent estimate of the p-values is proposed. Tests on artificial data and real-world forex data indicate that the new test procedure discovers dependence which is missed by linear approaches, while the earlier bootstrap procedure returns an elevated number of false positives.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-chwialkowski14, title = {A Kernel Independence Test for Random Processes}, author = {Chwialkowski, Kacper and Gretton, Arthur}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {1422--1430}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/chwialkowski14.pdf}, url = {https://proceedings.mlr.press/v32/chwialkowski14.html}, abstract = {A non-parametric approach to the problem of testing the independence of two random processes is developed. The test statistic is the Hilbert-Schmidt Independence Criterion (HSIC), which was used previously in testing independence for i.i.d. pairs of variables. The asymptotic behaviour of HSIC is established when computed from samples drawn from random processes. It is shown that earlier bootstrap procedures which worked in the i.i.d. case will fail for random processes, and an alternative consistent estimate of the p-values is proposed. Tests on artificial data and real-world forex data indicate that the new test procedure discovers dependence which is missed by linear approaches, while the earlier bootstrap procedure returns an elevated number of false positives.} }
Endnote
%0 Conference Paper %T A Kernel Independence Test for Random Processes %A Kacper Chwialkowski %A Arthur Gretton %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-chwialkowski14 %I PMLR %P 1422--1430 %U https://proceedings.mlr.press/v32/chwialkowski14.html %V 32 %N 2 %X A non-parametric approach to the problem of testing the independence of two random processes is developed. The test statistic is the Hilbert-Schmidt Independence Criterion (HSIC), which was used previously in testing independence for i.i.d. pairs of variables. The asymptotic behaviour of HSIC is established when computed from samples drawn from random processes. It is shown that earlier bootstrap procedures which worked in the i.i.d. case will fail for random processes, and an alternative consistent estimate of the p-values is proposed. Tests on artificial data and real-world forex data indicate that the new test procedure discovers dependence which is missed by linear approaches, while the earlier bootstrap procedure returns an elevated number of false positives.
RIS
TY - CPAPER TI - A Kernel Independence Test for Random Processes AU - Kacper Chwialkowski AU - Arthur Gretton BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/06/18 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-chwialkowski14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 2 SP - 1422 EP - 1430 L1 - http://proceedings.mlr.press/v32/chwialkowski14.pdf UR - https://proceedings.mlr.press/v32/chwialkowski14.html AB - A non-parametric approach to the problem of testing the independence of two random processes is developed. The test statistic is the Hilbert-Schmidt Independence Criterion (HSIC), which was used previously in testing independence for i.i.d. pairs of variables. The asymptotic behaviour of HSIC is established when computed from samples drawn from random processes. It is shown that earlier bootstrap procedures which worked in the i.i.d. case will fail for random processes, and an alternative consistent estimate of the p-values is proposed. Tests on artificial data and real-world forex data indicate that the new test procedure discovers dependence which is missed by linear approaches, while the earlier bootstrap procedure returns an elevated number of false positives. ER -
APA
Chwialkowski, K. & Gretton, A.. (2014). A Kernel Independence Test for Random Processes. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(2):1422-1430 Available from https://proceedings.mlr.press/v32/chwialkowski14.html.

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