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Submodular Maximization via Gradient Ascent: The Case of Deep Submodular Functions
We study the problem of maximizing deep submodular functions (DSFs) subject to a matroid constraint.
Greed is Still Good: Maximizing Monotone Submodular+Supermodular (BP) Functions
We analyze the performance of the greedy algorithm, and also a discrete semi-gradient based algorithm, for maximizing the sum of a suBmodular and suPermodular (BP) function (both of which are non-negative monotone non-decreasing) under two types of constraints, either a cardinality constraint or $p\geq 1$ matroid independence constraints.
Deep Submodular Functions
Lastly, we discuss strategies to learn DSFs, and define the classes of deep supermodular functions, deep difference of submodular functions, and deep multivariate submodular functions, and discuss where these can be useful in applications.
Mixed Robust/Average Submodular Partitioning: Fast Algorithms, Guarantees, and Applications
In the present paper, we bridge this gap, by proposing several new algorithms (including greedy, majorization-minimization, minorization-maximization, and relaxation algorithms) that not only scale to large datasets but that also achieve theoretical approximation guarantees comparable to the state-of-the-art.
Mixed Robust/Average Submodular Partitioning: Fast Algorithms, Guarantees, and Applications to Parallel Machine Learning and Multi-Label Image Segmentation
While the robust versions have been studied in the theory community, existing work has focused on tight approximation guarantees, and the resultant algorithms are not, in general, scalable to very large real-world applications.
