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

Jul 12, 2020

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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.

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The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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