WHInter: A Working set algorithm for High-dimensional sparse second order Interaction models
This work addresses scalability issues for researchers in genomics and similar fields dealing with high-dimensional sparse interaction models, though it is incremental as it builds on existing l1-regularised methods with specific optimizations.
The paper tackles the problem of learning sparse linear models with two-way interactions in high-dimensional settings, such as genomics, where existing methods fail to scale due to the quadratic explosion of candidate interactions. It presents WHInter, a working set algorithm that is shown to be more scalable and two orders of magnitude faster than state-of-the-art methods on simulated and real genetic data.
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.