# WHInter: A Working set algorithm for High-dimensional sparse second order Interaction models

##### schedule le mardi 22 mai 2018 de 10h45 à 11h45

Organisé par : Castillo, Fischer, Giulini, Gribkova, Levrard, Roquain, Sangnier

Intervenant : Marine Le Morvan (Mines ParisTech)
Lieu : UPMC, salle 15-16.201

Sujet : WHInter: A Working set algorithm for High-dimensional sparse second order Interaction models

Résumé :

Learning sparse linear models with two-way interactions is desirable in many application domains such as genomics. $\ell_1$-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 $\ell_1$-regularised problems with two-way interactions. 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.