Deep submodular functions form a subclass of submodular functions that share many of the properties and advantages of deep neural networks. Bilmes and Bai showed that facility location functions can be approximated with deep submodular functions. We prove that facility location functions are in fact contained in the class of deep submodular functions.

Bibtex entry:

@techreport{egresqp-19-01,

AUTHOR | = | {B{\'e}rczi, Krist{\'o}f and B{\'e}rczi-Kov{\'a}cs Ren{\'a}ta, Erika and L{\H o}rincz, Andr{\'a}s and Milacski Á., Zolt{\'a}n}, |

TITLE | = | {Facility location functions are deep submodular functions}, |

NOTE | = | {{\tt egres.elte.hu}}, |

INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |

YEAR | = | {2019}, |

NUMBER | = | {QP-2019-01} |