Dependent randomized rounding for clustering and partition systems with knapsack constraints
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866929339656830976 |
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| author | Harris, David G. Pensyl, Thomas Srinivasan, Aravind Trinh, Khoa |
| author_facet | Harris, David G. Pensyl, Thomas Srinivasan, Aravind Trinh, Khoa |
| contents | Clustering problems are fundamental to unsupervised learning. There is an increased emphasis on fairness in machine learning and AI; one representative notion of fairness is that no single demographic group should be over-represented among the cluster-centers. This, and much more general clustering problems, can be formulated with "knapsack" and "partition" constraints. We develop new randomized algorithms targeting such problems, and study two in particular: multi-knapsack median and multi-knapsack center. Our rounding algorithms give new approximation and pseudo-approximation algorithms for these problems. One key technical tool, which may be of independent interest, is a new tail bound analogous to Feige (2006) for sums of random variables with unbounded variances. Such bounds can be useful in inferring properties of large networks using few samples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1709_06995 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Dependent randomized rounding for clustering and partition systems with knapsack constraints Harris, David G. Pensyl, Thomas Srinivasan, Aravind Trinh, Khoa Data Structures and Algorithms Clustering problems are fundamental to unsupervised learning. There is an increased emphasis on fairness in machine learning and AI; one representative notion of fairness is that no single demographic group should be over-represented among the cluster-centers. This, and much more general clustering problems, can be formulated with "knapsack" and "partition" constraints. We develop new randomized algorithms targeting such problems, and study two in particular: multi-knapsack median and multi-knapsack center. Our rounding algorithms give new approximation and pseudo-approximation algorithms for these problems. One key technical tool, which may be of independent interest, is a new tail bound analogous to Feige (2006) for sums of random variables with unbounded variances. Such bounds can be useful in inferring properties of large networks using few samples. |
| title | Dependent randomized rounding for clustering and partition systems with knapsack constraints |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/1709.06995 |