A Scalable Conditional Independence Test for Nonlinear, Non-Gaussian Data

By J. Ramsey. 2014

56 citations recorded by the source corpus.

Many relations of scientific interest are nonlinear, and even in linear systems distributions are often non-Gaussian, for example in fMRI BOLD data. A class of search procedures for causal relations in high dimensional data relies on sample derived conditional independence decisions. The most common applications rely on Gaussian tests that can be systematically erroneous in nonlinear non-Gaussian cases. Recent work (Gretton et al. (2009), Tillman et al. (2009), Zhang et al. (2011)) has proposed conditional independence tests using Reproducing Kernel Hilbert Spaces (RKHS). Among these, perhaps the most efficient has been KCI (Kernel Conditional Independence, Zhang et al. (2011)), with computational requirements that grow effectively at least as O(N3), placing it out of range of large sample size analysis, and restricting its applicability to high dimensional data sets. We propose a class of O(N2) tests using conditional correlation independence (CCI) that require a few seconds on a standard workstation for tests that require tens of minutes to hours for the KCI method, depending on degree of parallelization, with similar accuracy. For accuracy on difficult nonlinear, non-Gaussian data sets, we also compare a recent test due to Harris & Drton (2012), applicable to nonlinear, non-Gaussian distributions in the Gaussian copula, as well as to partial correlation, a linear Gaussian test.

Subfields: Analytical Chemistry, Artificial Intelligence, Control and Systems Engineering

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Citations in the corpus

The hardness of conditional independence testing and the generalised covariance measure (2018, background): “Ramsey [40] suggests regressing X on Z and Y on Z and then testing for independence between the residuals.”
Fast Conditional Independence Test for Vector Variables with Large Sample Sizes (2018, methodology): “For similar reasons, the Conditional Correlation Independence test (CCI) [Ramsey, 2014] determines independence of X and Y by only checking whether cov ( f ( X ) , g ( Y )) = 0 for different choices of f, g taken from an (in practice, truncated) set of basis functions.”
Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets (2020, background): “…ﬂexibility of utilizing a wide and growing class of CI tests, from linear partial correlation (ParCorr) and non-parametric residual-based approaches [Ramsey, 2014, Runge et al., 2019b] to Kernel measures [Zhang et al., 2011], tests based on conditional mutual information [Runge, 2018b], and…”
Approximate Kernel-Based Conditional Independence Tests for Fast Non-Parametric Causal Discovery (2017, background): “Notice also that this situation is more general than the additive noise models proposed in (Ramsey, 2014), where we have X = g1(Z) + ε1, Y = g2(Z) + ε2.”
Gaussian Processes for Independence Tests with Non-iid Data in Causal Inference (2015, methodology): “However, CCI is based on a finite basis expansion, so consistency only holds in the limit as the number of basis functions goes to infinity along with the number of samples, whereas we use a consistent nonparametric regression method, so consistency holds in the large-sample limit.”