A Kernel Independence Test for Random Processes

By Kacper P. Chwialkowski, Arthur Gretton. 2014

65 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Finance, Statistics and Probability, Statistical Learning Theory

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “The authors impose mixing conditions on random processes under investigation (see Chwialkowski and Gretton (2014) for details).”
The Arrow of Time in Multivariate Time Series (2016, background): “We ﬁrst report a consistency results for HSIC for time dependent data (Chwialkowski and Gretton, 2014).”
A Wild Bootstrap for Degenerate Kernel Tests (2014, methodology): “This approach has the important advantage over [8] that it may be applied to all kernel-based tests for which V -statistics are employed, and not just for independence tests.”
Nonparametric Independence Testing for Small Sample Sizes (2014, methodology): “…are shown to fail to 1HSIC and HSIC − 2HSIC/n−C/n2 both converge to population HSIC at same rate determined by the dominant term (HSIC). detect dependence (some of them were used in previous papers on independence testing like [Gretton et al., 2007] and [Chwialkowski and Gretton, 2014]).”
M-Statistic for Kernel Change-Point Detection (2015, methodology): “relax the temporal independence assumption and extend M -statistics for dependent data by incorporating ideas from (Chwialkowski and Gretton, 2014).”
Gaussian Processes for Independence Tests with Non-iid Data in Causal Inference (2015, background): “…kernel cross-spectral density operator for characterizing independence between time series and Chwialkowski and Gretton [2014] explored the behavior of HSIC for random processes (e.g., time series data), showing a new consistent estimate of the p-value for non-iid data, but neither of these works…”
Measuring Association on Topological Spaces Using Kernels and Geometric Graphs (2020, background): “This is particularly useful in functional regression models (see [73] for a survey), in reallife machine learning and human behavior recognition (see [28]), measuring association between two stochastic processes (see [27]), etc.”
Large-scale kernel methods for independence testing (2016, methodology): “We note that Chwialkowski and Gretton (2014) (Lemma 2 and Theorem 1) proves a more general result, applicable to dependent observations under certain mixing conditions where the i.i.d. setting is a special case. Moreover, Rubenstein et al. (2015) (Theorem5 and 6) provides another elegant proof in th”