  Recent discussion of the success of feature selection methods has argued that
focusing on a relatively small number of features has been counterproductive.
Instead, it is suggested, the number of significant features can be in the
thousands or tens of thousands, rather than (as is commonly supposed at
present) approximately in the range from five to fifty. This change, in orders
of magnitude, in the number of influential features, necessitates alterations
to the way in which we choose features and to the manner in which the success
of feature selection is assessed. In this paper, we suggest a general approach
that is suited to cases where the number of relevant features is very large,
and we consider particular versions of the approach in detail. We propose ways
of measuring performance, and we study both theoretical and numerical
properties of the proposed methodology.
