On Conditional and Partial Correlation

By A. .. Lawrance. 1976

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Kernel-based Conditional Independence Test and Application in Causal Discovery (2011, background): “In that case, X ⊥⊥ Y | Z reduces to zero partial correlation or zero conditional correlation between X and Y given Z , which can be easily tested (for the links between partial correlation, conditional correlation, and CI, see Lawrance (1976)).”
A Scalable Conditional Independence Test for Nonlinear, Non-Gaussian Data (2014, unknown): “and Lawrance, 1976.) The framework of RKHS is replaced by a simpler set of mathematical ideas: The first is that X _||_ Y just in case cov(f(X), g(Y)) = 0 for all functions f and g, where X an”
Communication-Avoiding Optimization Methods for Distributed Massive-Scale Sparse Inverse Covariance Estimation (2017, background): “Under the assumption that the underlying data-generating distribution is multivariate normal, the partial correlation graph is precisely the conditional independence graph associated with the variables [27, 26, 7].”