High-throughput technologies for rapid measurement of vast numbers of biological variables offer the potential for highly discriminatory diagnosis and prognosis, however, high dimensionality together with small samples creates the need for feature selection, while at the same time making feature-selection algorithms less reliable. Feature selection must typically be carried out from among thousands of gene-expression features and in the context of a small sample (small number of microarrays). Two basic questions arise: (1) Can one expect feature selection to yield a feature set whose error is close to that of an optimal feature set? (2) If a good feature set is not found, should it be expected that good feature sets do not exist?