We propose a computationally intensive method, the random lasso method, for
variable selection in linear models. The method consists of two major steps. In
step 1, the lasso method is applied to many bootstrap samples, each using a set
of randomly selected covariates. A measure of importance is yielded from this
step for each covariate. In step 2, a similar procedure to the first step is
implemented with the exception that for each bootstrap sample, a subset of
covariates is randomly selected with unequal selection probabilities determined
by the covariates' importance.

In many engineering and scientific applications, prediction variables are
grouped, for example, in biological applications where assayed genes or
proteins can be grouped by biological roles or biological pathways. Common
statistical analysis methods such as ANOVA, factor analysis, and functional
modeling with basis sets also exhibit natural variable groupings.

Typical protocols for peer-to-peer file sharing over the Internet divide
files to be shared into pieces. New peers strive to obtain a complete
collection of pieces from other peers and from a seed. In this paper we
identify a problem that can occur if the seeding rate is not large enough. The
problem is that, even if the statistics of the system are symmetric in the
pieces, there can be symmetry breaking, with one piece becoming very rare. If
peers depart after obtaining a complete collection, they can tend to leave
before helping other peers receive the rare piece.