A tempting wrong turn

Topic: Graphical models · more questions on this topic
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A student draws a graph for gene-expression data by connecting every pair of genes whose sample correlation exceeds 0.5 in absolute value, and interprets the missing edges as conditional independences. What is wrong with this, and what should be used instead?

Worked answer (click to show)

In the Gaussian chain 1-2-3, the endpoints can have nonzero marginal covariance while being independent conditional on the middle variable. Thresholding marginal correlations estimates a different object from a concentration graph. It is not an indirect way to estimate the same missing-edge restrictions. Under the nonsingular Gaussian model, use the negative normalised precision entries for partial correlations. In high dimension, the graphical lasso or neighbourhood selection supplies an estimated sparse structure, whose tuning and sampling uncertainty still need assessment. The undirected graph itself identifies no causal direction.