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Convex Analysis for Minimizing and L...

Stobbe, Peter.

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Convex Analysis for Minimizing and Learning Submodular Set Functions.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Convex Analysis for Minimizing and Learning Submodular Set Functions./
Author:	Stobbe, Peter.
Description:	115 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-10(E), Section: B.
Contained By:	Dissertation Abstracts International74-10B(E).
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3567166
ISBN:	9781303188077

Convex Analysis for Minimizing and Learning Submodular Set Functions.
Stobbe, Peter.

Convex Analysis for Minimizing and Learning Submodular Set Functions. - 115 p.

Source: Dissertation Abstracts International, Volume: 74-10(E), Section: B.

Thesis (Ph.D.)--California Institute of Technology, 2013.

The connections between convexity and submodularity are explored, for purposes of minimizing and learning submodular set functions.

ISBN: 9781303188077Subjects--Topical Terms:

1669109
Applied Mathematics.

Convex Analysis for Minimizing and Learning Submodular Set Functions.
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008 150210s2013 ||||||||||||||||| ||eng d
020 $a 9781303188077
035 $a (MiAaPQ)AAI3567166
035 $a AAI3567166
040 $a MiAaPQ $c MiAaPQ
100 1 $a Stobbe, Peter. $3 2094170
245 1 0 $a Convex Analysis for Minimizing and Learning Submodular Set Functions.
300 $a 115 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-10(E), Section: B.
500 $a Adviser: Andreas Krause.
502 $a Thesis (Ph.D.)--California Institute of Technology, 2013.
520 $a The connections between convexity and submodularity are explored, for purposes of minimizing and learning submodular set functions.
520 $a First, we develop a novel method for minimizing a particular class of submodular functions, which can be expressed as a sum of concave functions composed with modular functions. The basic algorithm uses an accelerated first order method applied to a smoothed version of its convex extension. The smoothing algorithm is particularly novel as it allows us to treat general concave potentials without needing to construct a piecewise linear approximation as with graph-based techniques.
520 $a Second, we derive the general conditions under which it is possible to find a minimizer of a submodular function via a convex problem. This provides a framework for developing submodular minimization algorithms. The framework is then used to develop several algorithms that can be run in a distributed fashion. This is particularly useful for applications where the submodular objective function consists of a sum of many terms, each term dependent on a small part of a large data set.
520 $a Lastly, we approach the problem of learning set functions from an unorthodox perspective---sparse reconstruction. We demonstrate an explicit connection between the problem of learning set functions from random evaluations and that of sparse signals. Based on the observation that the Fourier transform for set functions satisfies exactly the conditions needed for sparse reconstruction algorithms to work, we examine some different function classes under which uniform reconstruction is possible.
590 $a School code: 0037.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Computer Science. $3 626642
650 4 $a Operations Research. $3 626629
690 $a 0364
690 $a 0984
690 $a 0796
710 2 $a California Institute of Technology. $b Applied and Computational Mathematics. $3 2094171
773 0 $t Dissertation Abstracts International $g 74-10B(E).
790 $a 0037
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3567166