Seminar Details
2018-10-09 (14:00) : Fast and invariant learning for Independent Component Analysis
At Euler building (room A.002)
Organized by Mathematical Engineering
Speakers :
Jean-François Cardoso (CNRS - INRIA)
,
and
Ablin, Pierre
Abstract :
Independent Component Analysis (ICA) is a widely used unsupervised data exploration technique. It models a set of observed signals as a linear mixtures of statistically independent sources and aims at recovering blindly those underlying sources. Here `blind' means that sources are recovered from the signals by applying a separating matrix which is totally inconstrained, making ICA applicable in a large variety of tasks.
After a brief introduction, we stress the multiplicative structure of the ICA problem: the parameter space is the multiplicative group of GL(n) of square invertible matrices. Learning algorithms which exploit this structure are `equivariant' and are `rewarded' for doing so in terms implementation, optimization and performance, as we shall see.
In a second part, we introduce a fast quasi-Newton equivariant algorithm for ICA, the Preconditioned ICA for Real Data (Picard) algorithm. It exploits the specific structure of the problem to compute cheap Hessian approximations, and then refines them using L-BFGS, a classical optimization algorithm. It shows state of the art convergence speed when applied to real datasets. Interestingly, it can be straightforwardly constrained to work on the rotation manifold, a constraint often imposed in ICA.