independence-tests {bnlearn}

Conditional independence tests

Description

Overview of the conditional independence tests implemented in bnlearn, with the respective reference publications.

Details

Unless otherwise noted, the reference publication for conditional independence tests is:

Edwards DI (2000). Introduction to Graphical Modelling. Springer, 2nd edition.

Additionally for continuous permutation tests:

Legendre P (2000). "Comparison of Permutation Methods for the Partial Correlation and Partial Mantel Tests". Journal of Statistical Computation and Simulation, 67:37–73.

and for semiparametric discrete tests:

Tsamardinos I, Borboudakis G (2010). "Permutation Testing Improves Bayesian Network Learning". Machine Learning and Knowledge Discovery in Databases, 322–337.

Available conditional independence tests (and the respective labels) for discrete Bayesian networks (categorical variables) are:

• mutual information: an information-theoretic distance measure. It's proportional to the log-likelihood ratio (they differ by a 2n factor) and is related to the deviance of the tested models. The asymptotic \chi^2 test (mi and mi-adf, with adjusted degrees of freedom), the Monte Carlo permutation test (mc-mi), the sequential Monte Carlo permutation test (smc-mi), and the semiparametric test (sp-mi) are implemented.

• shrinkage estimator for the mutual information (mi-sh): an improved asymptotic \chi^2 test based on the James-Stein estimator for the mutual information.

  Hausser J, Strimmer K (2009). "Entropy inference and the James-Stein estimator, with application to nonlinear gene association networks". Statistical Applications in Genetics and Molecular Biology, 10:1469–1484.

• Pearson's X^2: the classical Pearson's X^2 test for contingency tables. The asymptotic \chi^2 test (x2 and x2-adf, with adjusted degrees of freedom), the Monte Carlo permutation test (mc-x2), the sequential Monte Carlo permutation test (smc-x2) and semiparametric test (sp-x2) are implemented.

Available conditional independence tests (and the respective labels) for discrete Bayesian networks (ordered factors) are:

• Jonckheere-Terpstra: a trend test for ordinal variables. The asymptotic normal test (jt), the Monte Carlo permutation test (mc-jt) and the sequential Monte Carlo permutation test (smc-jt) are implemented.

Available conditional independence tests (and the respective labels) for Gaussian Bayesian networks (normal variables) are:

• linear correlation: Pearson's linear correlation. The exact Student's t test (cor), the Monte Carlo permutation test (mc-cor) and the sequential Monte Carlo permutation test (smc-cor) are implemented.

  Hotelling H (1953). "New Light on the Correlation Coefficient and its Transforms". Journal of the Royal Statistical Society: Series B, 15(2):193–225.

• Fisher's Z: a transformation of the linear correlation with asymptotic normal distribution. The asymptotic normal test (zf), the Monte Carlo permutation test (mc-zf) and the sequential Monte Carlo permutation test (smc-zf) are implemented.

• mutual information: an information-theoretic distance measure. Again it is proportional to the log-likelihood ratio (they differ by a 2n factor). The asymptotic \chi^2 test (mi-g), the Monte Carlo permutation test (mc-mi-g) and the sequential Monte Carlo permutation test (smc-mi-g) are implemented.

• shrinkage estimator for the mutual information (mi-g-sh): an improved asymptotic \chi^2 test based on the James-Stein estimator for the mutual information.

  Ledoit O, Wolf M (2003). "Improved Estimation of the Covariance Matrix of Stock Returns with an Application to Portfolio Selection". Journal of Empirical Finance, 10:603–621.

Available conditional independence tests (and the respective labels) for hybrid Bayesian networks (mixed discrete and normal variables) are:

• mutual information: an information-theoretic distance measure. Again it is proportional to the log-likelihood ratio (they differ by a 2n factor). Only the asymptotic \chi^2 test (mi-cg) is implemented.