In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a large volume of work devoted to the study of submodular functions in recent years, the vast majority of this work has been focused on algorithms that output sets, not sequences. However, in many settings, the order in which we output items can be just as important as the items themselves. To extend the notion of submodularity to sequences, we use a directed graph on the items where the edges encode the additional value of selecting items in a particular order. Existing theory is limited to the case where this underlying graph is a directed acyclic graph. In this paper, we introduce two new algorithms that provably give constant factor approximations for general graphs and hypergraphs having bounded in or out degrees. Furthermore, we show the utility of our new algorithms for real-world applications in movie recommendation, online link prediction, and the design of course sequences for MOOCs.
|Number of pages||8|
|State||Published - 2018|
|Event||21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018 - Playa Blanca, Lanzarote, Canary Islands, Spain|
Duration: 9 Apr 2018 → 11 Apr 2018
|Conference||21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018|
|City||Playa Blanca, Lanzarote, Canary Islands|
|Period||9/04/18 → 11/04/18|
Bibliographical noteFunding Information:
Acknowledgements We acknowledge support from DARPA YFA (D16AP00046), AFOSR YIP (FA9550-18-1-0160), and ISF grant 1357/16.
We acknowledge support from DARPA YFA (D16AP00046), AFOSR YIP (FA9550-18-1-0160), and ISF grant 1357/16.
Copyright 2018 by the author(s).