From Sets to Multisets: Provable Variational Inference for Probabilistic Integer Submodular Models

Part of Proceedings of the International Conference on Machine Learning 1 pre-proceedings (ICML 2020)

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Authors

Aytunc Sahin, Yatao Bian, Joachim Buhmann, Andreas Krause

Abstract

<p>Submodular functions have been studied extensively in machine learning and data mining. In particular, the optimization of submodular functions over the integer lattice has recently attracted much interest, because this domain relates naturally to many practical problem settings, such as multilabel graph cut, budget allocation and revenue maximization with discrete assignments. In contrast, the use of these functions for probabilistic modeling has received surprisingly little attention so far. In this work, we firstly propose the Generalized Multilinear Extension, a continuous DR-Submodular extension for integer submodular functions. We study central properties of this extension and formulate a new probabilistic model which is defined through integer submodular functions. Then, we introduce a method to perform approximate inference for those class of models. Finally, we demonstrate its effectiveness and viability on several real-world social connection graph datasets with integer submodular objectives.</p>