Oral
Constrained Interacting Submodular Groupings
Andrew Cotter · Mahdi Milani Fard · Seungil You · Maya Gupta · Jeff Bilmes

Thu Jul 12th 04:40 -- 04:50 PM @ K11

We introduce the problem of grouping a finite ground set into blocks where each block is a subset of the ground set and where: (i) the blocks are individually highly valued by a submodular function (both robustly and in the average case) while satisfying block-specific matroid constraints; and (ii) block scores interact where blocks are jointly scored highly, thus making the blocks mutually non-redundant. Submodular functions are good models of information and diversity; thus, the above can be seen as grouping the ground set into matroid constrained blocks that are both intra- and inter-diverse. Potential applications include forming ensembles of classification/regression models, partitioning data for parallel processing, and summarization. In the non-robust case, we reduce the problem to non-monotone submodular maximization subject to multiple matroid constraints. In the mixed robust/average case, we offer a bi-criterion guarantee for a polynomial time deterministic algorithm and a probabilistic guarantee for randomized algorithm, as long as the involved submodular functions (including the inter-block interaction terms) are monotone. We close with a case study in which we use these algorithms to find high quality diverse ensembles of classifiers, showing good results.

Author Information

Andrew Cotter (Google AI)
Mahdi Milani Fard (Google)
Seungil You (Google)
Maya Gupta (Google)
Jeff Bilmes (UW)

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