ÍâÍøÌìÌÃ

Parsimony, including sparsity and low rank, has been shown to successfully modelÌýdata in numerous machine learning and signal processing tasks. Traditionally, suchÌýmodeling approaches rely on an iterative algorithm that minimizes an objectiveÌýfunction with parsimony-promoting terms. The inherently sequential structure andÌýdata-dependent complexity and latency of iterative optimization constitute a majorÌýlimitation in many applications requiring real-time performance or involving large scale data.ÌýAnother limitation encountered by these modeling techniques is theÌýdifficulty of their inclusion in discriminative learning scenarios. In this work, weÌýpropose to move the emphasis from the model to the pursuit algorithm, and develop aÌýprocess-centric view of parsimonious modeling, in which a learned deterministicÌýfixed-complexity pursuit process is used in lieu of iterative optimization. We show aÌýprincipled way to construct learnable pursuit process architectures for structuredÌýsparse and robust low rank models, derived from the iteration of proximal descentÌýalgorithms. These architectures learn to approximate the exact parsimoniousÌýrepresentation at a fraction of the complexity of the standardÌýoptimization methods.ÌýWe also show that appropriate training regimes allow to naturally extendÌýparsimonious models to discriminative settings. State-of-the-art results areÌýdemonstrated on several challenging problems in image and audio processing withÌýseveral orders of magnitude speedup compared to the exact optimization algorithms.ÌýJoint work with P. Sprechmann and A. Bronstein.