Title: WHInter: A Working set algorithm for High-dimensional sparse second order Interaction models,
Abstract: Learning sparse linear models with two-way interactions is desirable in many
application domains such as genomics. l1-regularised linear models are popular
to estimate sparse models, yet standard implementations fail to address
specifically the quadratic explosion of candidate two-way interactions in high
dimensions, and typically do not scale to genetic data with hundreds of
thousands of features. Here we present WHInter, a working set algorithm to
solve large l1-regularised problems with two-way interactions for binary design
matrices. The novelty of WHInter stems from a new bound to efficiently identify
working sets while avoiding to scan all features, and on fast computations
inspired from solutions to the maximum inner product search problem. We apply
WHInter to simulated and real genetic data and show that it is more scalable
and two orders of magnitude faster than the state of the art.