Constrained Interacting Submodular Groupings

Andrew Cotter, Mahdi Milani Fard, Seungil You, Maya Gupta, Jeff Bilmes
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:1068-1077, 2018.

Abstract

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.

Cite this Paper


BibTeX
@InProceedings{pmlr-v80-cotter18a, title = {Constrained Interacting Submodular Groupings}, author = {Cotter, Andrew and Fard, Mahdi Milani and You, Seungil and Gupta, Maya and Bilmes, Jeff}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {1068--1077}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/cotter18a/cotter18a.pdf}, url = {http://proceedings.mlr.press/v80/cotter18a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Constrained Interacting Submodular Groupings %A Andrew Cotter %A Mahdi Milani Fard %A Seungil You %A Maya Gupta %A Jeff Bilmes %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-cotter18a %I PMLR %P 1068--1077 %U http://proceedings.mlr.press/v80/cotter18a.html %V 80 %X 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.
APA
Cotter, A., Fard, M.M., You, S., Gupta, M. & Bilmes, J.. (2018). Constrained Interacting Submodular Groupings. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:1068-1077 Available from http://proceedings.mlr.press/v80/cotter18a.html.

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