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VERSION:2.0
PRODID:-//Memento EPFL//
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SUMMARY:Structured Sparsity-inducing Norms through Submodular Functions
DTSTART:20110203T161500
DTSTAMP:20260407T033940Z
UID:ae1784452b34d25f1310cfd5d6f5707dc3e3867e6bbcb67d08b5116a
CATEGORIES:Conferences - Seminars
DESCRIPTION:Francis Bach\, Ecole Normale Supérieure\, Paris\nSparse metho
 ds for supervised learning aim at finding good linear predictors from as f
 ew variables as possible\, i.e.\, with small cardinality of their supports
 . This combinatorial selection problem is often turned into a convex optim
 ization problem by replacing the cardinality function by its convex envelo
 pe (tightest convex lower bound)\, in this case the L1-norm. In this paper
 \, we investigate more general set-functions than the cardinality\, that m
 ay incorporate prior knowledge or structural constraints which are common 
 in many applications: namely\, we show that for nondecreasing submodular s
 et-functions\, the corresponding convex envelope can be obtained from its 
 Lovasz extension\, a common tool in submodular analysis. This defines a fa
 mily of polyhedral norms\, for which we provide generic algorithmic tools 
 (subgradients and proximal operators) and theoretical results (conditions 
 for support recovery or high-dimensional inference). By selecting specific
  submodular functions\, we can give a new interpretation to known norms\, 
 such as those based on rank-statistics or grouped norms with potentially o
 verlapping groups\; we also define new norms\, in particular ones that can
  be used as non-factorial priors for supervised learning. 
LOCATION:MX F1
STATUS:CONFIRMED
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