arXiv Machine Learning By Lucas D. Konrad, Nikolas Kuschnig

Finding Most Influential Sets

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arXiv:2606. 05919v1 Announce Type: cross Abstract: Identifying most influential sets (MIS) - size-$k$ subsets whose removal maximally changes a target estimand - is typically infeasible because it requires searching over $\binom{n}{k}$ subsets.

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arXiv Machine Learning
Oct 22

Supermodular Rank: Set Function Decomposition and Optimization

The paper introduces the concept of supermodular rank, defined as the minimal number of supermodular components required to express a function on a lattice. It characterizes the maximum possible rank and the structure of functions with a fixed rank, and analogously defines submodular rank. Leveraging submodular decompositions, the authors propose an algorithm that partitions a set‑function optimization problem into submodular subproblems, thereby improving approximation guarantees for monotone maximization and ratio minimization while incurring a computational cost tied to the submodular rank.

By Rishi Sonthalia, Anna Seigal, Guido Montufar