Cut Pursuit: fast algorithms to learn piecewise constant functions

Loic Landrieu 1, 2, 3, 4 Guillaume Obozinski 1, 2, 3
2 IMAGINE [Marne-la-Vallée]
LIGM - Laboratoire d'Informatique Gaspard-Monge, CSTB - Centre Scientifique et Technique du Bâtiment, ENPC - École des Ponts ParisTech
4 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : We propose working-set/greedy algorithms to efficiently find the solutions to convex optimization problems penalized respectively by the total variation and the Mumford Shah boundary size. Our algorithms exploit the piecewise constant structure of the level-sets of the solutions by recursively splitting them using graph cuts. We obtain significant speed up on images that can be approximated with few level-sets compared to state-of-the-art algorithms .
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Loic Landrieu, Guillaume Obozinski. Cut Pursuit: fast algorithms to learn piecewise constant functions. 19th International Conference on Artificial Intelligence and Statistics (AISTATS 2016) , May 2016, Cadix, Spain. ⟨hal-01306786⟩

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