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Structured Sparsity Inducing Norms: Statistical and Algorithmic Properties with

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99 pages
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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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
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
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]
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
he example of neuroimaging ore than just cardinality! hstructuralinformation
Structure? T In practice, know m Sparsity comes wit
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
Structure? Other motivating examples
Spatial: Bioinformatics: contiguity due to the genome organization [Rapaport et al., 2008]  pixels [Boykov et al., 2001] neighboringImage segmentation:
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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