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Abstract:
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The graphical lasso is often used to model the dependence structure between variables. However, inferential questions about the resulting solution have traditionally been difficult to answer. We discuss the problem of testing the significance of edges that are present in the graphical lasso solution. We present a solution that accounts for the graph selection procedure and produces valid statistical tests despite the fact that the selection was carried out on the same data. The test is difficult to evaluate analytically, so we instead present a Markov Chain Monte Carlo sampling scheme to carry out the inference. The resulting test sheds some light on the reliability of the specific edges in the graphical lasso solution, and also has connections to both hierarchical clustering and other recent work in selective inference.
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