On approximate non-submodular minimization via tree-structured supermodularity

Yoshinobu Kawahara, Rishabh Iyer, Jeffery A. Bilmes

Research output: Contribution to journalConference article

1 Citation (Scopus)

Abstract

We address the problem of minimizing non-submodular functions where the supermodularity is restricted to tree-structured pair-wise terms. We are motivated by several real world applications, which require submodu-larity along with structured supermodular-ity, and this forms a rich class of expressive models, where the non-submodularity is restricted to a tree. While this problem is NP hard (as we show), we develop several practical algorithms to find approximate and near-optimal solutions for this problem, some of which provide lower and others of which provide upper bounds thereby allowing us to compute a tightness gap. We also show that some of our algorithms can be extended to handle more general forms of supermodular-ity restricted to arbitrary pairwise terms. We compare our algorithms on synthetic data, and also demonstrate the advantage of the formulation on the real world application of image segmentation, where we incorporate structured supermodularity into higher-order submodular energy minimization.

Original languageEnglish
Pages (from-to)444-452
Number of pages9
JournalJournal of Machine Learning Research
Volume38
Publication statusPublished - Jan 1 2015
Externally publishedYes
Event18th International Conference on Artificial Intelligence and Statistics, AISTATS 2015 - San Diego, United States
Duration: May 9 2015May 12 2015

Fingerprint

Supermodularity
Real-world Applications
Energy Minimization
Tightness
Term
Synthetic Data
Image segmentation
Image Segmentation
Pairwise
Computational complexity
NP-complete problem
Optimal Solution
Higher Order
Upper bound
Formulation
Arbitrary
Demonstrate
Form
Model

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

Cite this

On approximate non-submodular minimization via tree-structured supermodularity. / Kawahara, Yoshinobu; Iyer, Rishabh; Bilmes, Jeffery A.

In: Journal of Machine Learning Research, Vol. 38, 01.01.2015, p. 444-452.

Research output: Contribution to journalConference article

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