2015/11/06 by Jennifer Gillenwater, Gillenwater, Jennifer, Rishabh Iyer +7 · 8 citations
Computer Science · Mathematics · #Algorithm #Artificial Intelligence (cs.AI) #Block code #Combinatorics #Complexity and Algorithms in Graphs #Computer science #Cryptography and Data Security #Data Structures and Algorithms (cs.DS) #Decoding methods #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Hamming code #Hamming distance #Hamming graph #Mathematics #Stochastic Gradient Optimization Techniques #Submodular set function #cs.AI #cs.DM #cs.DS
paper · pdf · doi:10.48550/arxiv.1511.02163
published in arXiv (Cornell University) (Cornell University) · 15 pages, 1 figure, a short version of this will appear in the NIPS 2015 conference
arxiv created 2015/11/06 · openalex publication_date 2015/11/06 · arxiv updated 2015/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that there is a largely unexplored class of functions (positive polymatroids) that can define proper discrete metrics over pairs of binary vectors and that are fairly tractable to optimize over. By exploiting submodularity, we are able to give hardness results and approximation algorithms for optimizing over such metrics. Additionally, we demonstrate empirically the effectiveness of these metrics and associated algorithms on both a metric minimization task (a form of clustering) and also a metric maximization task (generating diverse k-best lists).