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 language | English |
|---|---|
| Pages (from-to) | 444-452 |
| Number of pages | 9 |
| Journal | Journal of Machine Learning Research |
| Volume | 38 |
| Publication status | Published - Jan 1 2015 |
| Externally published | Yes |
| Event | 18th International Conference on Artificial Intelligence and Statistics, AISTATS 2015 - San Diego, United States Duration: May 9 2015 → May 12 2015 |
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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 journal › Conference article
}
TY - JOUR
T1 - On approximate non-submodular minimization via tree-structured supermodularity
AU - Kawahara, Yoshinobu
AU - Iyer, Rishabh
AU - Bilmes, Jeffery A.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=84954316178&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:84954316178
VL - 38
SP - 444
EP - 452
JO - Journal of Machine Learning Research
JF - Journal of Machine Learning Research
SN - 1532-4435
ER -