A Statistical View of Column Subset Selection
Anav Sood Trevor Hastie
We consider the problem of selecting a small subset of representative
variables from a large dataset. In the computer science literature, this
dimensionality reduction problem is typically formalized as Column Subset
Selection (CSS). Meanwhile, the typical statistical formalization is to find an
information-maximizing set of Principal Variables. This paper shows that these
two approaches are equivalent, and moreover, both can be viewed as maximum
likelihood estimation within a certain semi-parametric model. Using these
connections, we show how to efficiently (1) perform CSS using only summary
statistics from the original dataset; (2) perform CSS in the presence of
missing and/or censored data; and (3) select the subset size for CSS in a
hypothesis testing framework.