Learning with Submodular Functions: A Convex Optimization Perspective - Inria - Institut national de recherche en sciences et technologies du numérique
Books Year : 2013

Learning with Submodular Functions: A Convex Optimization Perspective

Abstract

Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the lovasz extension of submodular functions provides a useful set of regularization functions for supervised and unsupervised learning. In this monograph, we present the theory of submodular functions from a convex analysis perspective, presenting tight links between certain polyhedra, combinatorial optimization and convex optimization problems. In particular, we show how submodular function minimization is equivalent to solving a wide variety of convex optimization problems. This allows the derivation of new efficient algorithms for approximate and exact submodular function minimization with theoretical guarantees and good practical performance. By listing many examples of submodular functions, we review various applications to machine learning, such as clustering, experimental design, sensor placement, graphical model structure learning or subset selection, as well as a family of structured sparsity-inducing norms that can be derived and used from submodular functions.
Fichier principal
Vignette du fichier
submodular_fot_revised_hal.pdf (3.19 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-00645271 , version 1 (27-11-2011)
hal-00645271 , version 2 (07-10-2013)

Identifiers

Cite

Francis Bach. Learning with Submodular Functions: A Convex Optimization Perspective. Now Publishers, pp.228, 2013, Foundations and Trends in Machine Learning, 978-1-60198-756-3. ⟨10.1561/2200000039⟩. ⟨hal-00645271v2⟩
4506 View
2637 Download

Altmetric

Share

More