Title: Forward-Backward Selection with Early Dropping,
Abstract: Forward-backward selection is one of the most basic and commonly-used feature
selection algorithms available. It is also general and conceptually applicable
to many different types of data. In this paper, we propose a heuristic that
significantly improves its running time, while preserving predictive accuracy.
The idea is to temporarily discard the variables that are conditionally
independent with the outcome given the selected variable set. Depending on how
those variables are reconsidered and reintroduced, this heuristic gives rise to
a family of algorithms with increasingly stronger theoretical guarantees. In
distributions that can be faithfully represented by Bayesian networks or
maximal ancestral graphs, members of this algorithmic family are able to
correctly identify the Markov blanket in the sample limit. In experiments we
show that the proposed heuristic increases computational efficiency by about
two orders of magnitude in high-dimensional problems, while selecting fewer
variables and retaining predictive performance. Furthermore, we show that the
proposed algorithm and feature selection with LASSO perform similarly when
restricted to select the same number of variables, making the proposed
algorithm an attractive alternative for problems where no (efficient) algorithm
for LASSO exists.