Structured Sparsity Inducing Norms: Statistical and Algorithmic Properties with

Rodolphe Jenatton

Description

Structured Sparsity-Inducing Norms: Statistical and Algorithmic Properties with Applications to Neuroimaging Rodolphe Jenatton SIERRA project, INRIA Rocquencourt - Ecole Normale Superieure PhD defense at ENS Cachan, November 24, 2011 Advisors: Jean-Yves Audibert Francis Bach Reviewers: Laurent El Ghaoui Massimiliano Pontil Examinateurs: Remi Gribonval Eric Moulines Guillaume Obozinski Bertrand Thirion

• structured sparsity-inducing


• ens cachan


• prior knowledge only


• rocquencourt - ecole normale


• sparsity

Sujets

• Audibert
• Pontil
• Moulines
• Michel

Informations

• Publié par: pefav
• Nombre de lectures: 19
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Structured Sparsity-Inducing Statistical and Algorithmic Prop Applications to Neuroima

Norms: erties w ging

ith

Rodolphe Jenatton SIERRAproject,INRIARocquencourt-EcoleNormaleSupe´rieure

PhD defense at ENS Cachan, November 24, 2011

Advisors: Jean-Yves Audibert Francis Bach Reviewers: Laurent El Ghaoui Massimiliano Pontil

Examinateurs: R´emiGribonval Eric Moulines Guillaume Obozinski Bertrand Thirion

Francis Bach

Bertrand Thirion

R´emiGribonval

Jean-Yves Audibert

Alexandre Gramfort

SIERRA/WILLOW

Acknowledgments

Guillaume Obozinski

Gae¨lVaroqueaux

Julien Mairal

Vincent Michel

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Sparsity

Important concept in statistics, machine learning,. . . • Favour “simple models” • Easier interpretation, cheaper post-processing • Models with few parameters,feature selection

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Sparsity

Important concept in statistics, machine learning,. . . • Favour “simple models” • Easier interpretation, cheaper post-processing • Models with few parameters,feature selection

A

pplications: • Compressed sensing [Candes and Tao, 2005] • calmaphiGruaesnihs[seMdole20n,anlmuhB¨ndna]60 • Signal/image processing tasks • E.g., denoising [Chen et al., 1998; Mairal, 2010]

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Sparsity

Important concept in statistics, machine learning,. . . • Favour “simple models ” • Easier interpretation, cheaper post-processing • Models with few parameters,feature selection

A

pplications: • Compressed sensing [Candes and Tao, 2005] • nlns,[2MhmlomdaedhBa¨uuseeniannsGcila0a0r]h6p • Signal/image processing tasks • E.g., denoising [Chen et al., 1998; Mairal, 2010]

Disregards structure: • Prior knowledge only aboutcardinality

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he example of neuroimaging ore than just cardinality! hstructuralinformation

Structure? T In practice, know m Sparsity comes wit

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Structure? The example of neuroimaging In practice, know more than just cardinality! Sparsity comes withstructuralinformation

Spatial structurein neuroimaging [Chklovskii and Koulakov, 2004; Gramfort et al., 2011] •  discriminative voxelsSparsity: few • Spatiality: clusters according to the geometry of the brain

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Structure? Other motivating examples

Spatial: • Bioinformatics: contiguity due to the genome organization [Rapaport et al., 2008] •  pixels [Boykov et al., 2001] neighboringImage segmentation:

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Structure?

Other motivating examples

Spatial: • Bioinformatics: contiguity due to the genome organization [Rapaport et al., 2008] •  pixels [Boykov et al., 2001]Image segmentation: neighboring Temporal: • expressions [Tibau Puig et al., 2011]Time series of gene