On approximate non-submodular minimization via tree-structured supermodularity

Yoshinobu Kawahara, Rishabh Iyer, Jeffery A. Bilmes

Research output: Contribution to journalConference articlepeer-review

2 Citations (Scopus)


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
Publication statusPublished - 2015
Externally publishedYes
Event18th International Conference on Artificial Intelligence and Statistics, AISTATS 2015 - San Diego, United States
Duration: May 9 2015May 12 2015

All Science Journal Classification (ASJC) codes

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


Dive into the research topics of 'On approximate non-submodular minimization via tree-structured supermodularity'. Together they form a unique fingerprint.

Cite this