Robust Submodular Minimization with Applications to Cooperative Modeling

TL;DR

This paper introduces scalable algorithms for robust submodular minimization under various combinatorial constraints, with applications in image segmentation and matching, demonstrating effectiveness on synthetic and real datasets.

Contribution

First to study robust submodular minimization with broad combinatorial constraints, providing approximation algorithms and hardness bounds.

Findings

Algorithms achieve good approximation ratios.

Methods are scalable to large datasets.

Empirical results validate practical utility.

Abstract

Robust Optimization is becoming increasingly important in machine learning applications. This paper studies the problem of robust submodular minimization subject to combinatorial constraints. Constrained Submodular Minimization arises in several applications such as co-operative cuts in image segmentation, co-operative matchings in image correspondence, etc. Many of these models are defined over clusterings of data points (for example pixels in images), and it is important for these models to be robust to perturbations and uncertainty in the data. While several existing papers have studied robust submodular maximization, ours is the first work to study the minimization version under a broad range of combinatorial constraints including cardinality, knapsack, matroid as well as graph-based constraints such as cuts, paths, matchings, and trees. In each case, we provide scalable approximation algorithms and also study hardness bounds. Finally, we empirically demonstrate the utility of our algorithms on synthetic and real-world datasets.