Logistic lasso
Section of High-dimensional analysis, part of Statistical learning
Logistic lasso
| Type | Section |
| Taught in | High-dimensional analysis |
| Part | Statistical learning |
The lasso was used to perform model selection at the same time as fitting a logistic regression of the class on all the genes. The binomial deviance was the cost, with \lambda chosen as the value with the lowest binomial deviance on left-out data by cross-validation. This selected 14 gene indices
14,\;249,\;377,\;493,\;576,\;625,\;792,\;1360,\;1473,\;1582,\;1679,\;1772,\;1843,\;1924,
with fitted coefficients, in the same order,
\begin{aligned} &-0.111,\;-0.081,\;-0.588,\;-0.275,\;0.136,\;0.118,\;-0.116,\\ &0.089,\;0.113,\;0.085,\;0.141,\;0.302,\;-0.207,\;-0.141. \end{aligned}
The largest in magnitude are gene 377 (-0.588) and gene 1772 (+0.302), and the smallest is gene 249 (-0.081). Eleven of these were on the false-discovery list (14, 249, 377, 493, 625, 1473, 1582, 1679, 1772, 1843, 1924) and two were on the third-component list (493, 625).
The reported list contains 173 genes. A laboratory able to follow up only ten might prioritise the overlap with the lasso list and then apply an additional ranking. One such prioritisation retains genes 14, 377, 493, 625, 1473, 1582, 1679, 1772, 1843, 1924 after removing gene 249 from the eleven-gene overlap. This is a prioritisation rule, not a new false-discovery theorem: an arbitrary data-dependent subset of the discoveries need not inherit the original bound. Replication, measurement quality, and biological follow-up can test the candidates. The current data do not establish a causal role for them.
A principal-component analysis of the matrix followed by a lasso on the component scores selects combinations of all the genes, since each component is already a combination of all 2000 genes. That does not answer which genes. A lasso on the genes themselves is the fit that matches the question.
Used in
See also
Rank bound · Family-wise control implies false-discovery control · Benjamini–Hochberg · Benjamini–Hochberg controls the false discovery rate · Why classical methods fail when p > n · Rank of the sample covariance · Regression when p > n · Where high-dimensional columns come from