  In this paper, we study randomized reduction methods, which reduce
high-dimensional features into low-dimensional space by randomized methods
(e.g., random projection, random hashing), for large-scale high-dimensional
classification. Previous theoretical results on randomized reduction methods
hinge on strong assumptions about the data, e.g., low rank of the data matrix
or a large separable margin of classification, which hinder their applications
in broad domains. To address these limitations, we propose dual-sparse
regularized randomized reduction methods that introduce a sparse regularizer
into the reduced dual problem. Under a mild condition that the original dual
solution is a (nearly) sparse vector, we show that the resulting dual solution
is close to the original dual solution and concentrates on its support set. In
numerical experiments, we present an empirical study to support the analysis
and we also present a novel application of the dual-sparse regularized
randomized reduction methods to reducing the communication cost of distributed
learning from large-scale high-dimensional data.
