Fifteen genes from the colon-cancer screen
Section of Graphical models, part of Statistical learning
Fifteen genes from the colon-cancer screen
| Type | Section |
| Taught in | Graphical models |
| Part | Statistical learning |
A graphical-lasso analysis has also been reported for the fifteen genes with the smallest marginal p-values in the Alon analysis on the high-dimensional page. The processed file is absent, so the figures below are reported results, not fits recomputed here. Approximate normality of each marginal variable would not establish joint multivariate normality. Pooling tumour and normal tissue, and selecting variables using the same data, add further qualifications to a population interpretation.
The reported average absolute marginal correlation is near 0.46. Normalised precision entries of -0.52 are reported for genes 1843 and 1494, and +0.47 for genes 625 and 1635. Remember the sign reversal: a negative precision entry corresponds to positive partial correlation. After graphical-lasso selection using the extended criterion with \gamma=0.5, the first pair reportedly has normalised precision -0.42. The gene indices are 1494 and 1843. Reading truncated labels 149 and 184 would point at genes that are not among the fifteen analysed. An estimated zero, such as the reported entry for genes 1042 and 377, is a restriction in the fitted Gaussian model. It is not independent evidence that the biological variables are conditionally independent in the population. Shrinkage, selection, sampling variation, and misspecification can all affect the graph.
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See also
Undirected graph · Hammersley–Clifford · A zero precision entry is conditional independence · Maximum likelihood for a known graph · Graphical lasso · Markov graphs · Graph terminology · Conditional independence