Structured Sparsity Inducing Norms: Statistical and Algorithmic Properties with

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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

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Publié par

pefav

Nombre de lectures

Langue

English

Poids de l'ouvrage

1 Mo

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

•

Sparsity

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

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]

•

Sparsity

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

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

• •

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

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