Optimal Polynomial-Time Estimators: A Bayesian Notion of Approximation Algorithm
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866911023327346688 |
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| author | Kosoy, Vanessa Appel, Alexander |
| author_facet | Kosoy, Vanessa Appel, Alexander |
| contents | We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that cannot be solved exactly is uncertain and therefore should be described by a random variable. It thus should make sense to talk about the expected value of this random variable, an idea we formalize in the language of average-case complexity theory by introducing the concept of "optimal polynomial-time estimators." We prove some existence theorems and completeness results, and show that optimal polynomial-time estimators exhibit many parallels with "classical" probability theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1608_04112 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Optimal Polynomial-Time Estimators: A Bayesian Notion of Approximation Algorithm Kosoy, Vanessa Appel, Alexander Computational Complexity We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that cannot be solved exactly is uncertain and therefore should be described by a random variable. It thus should make sense to talk about the expected value of this random variable, an idea we formalize in the language of average-case complexity theory by introducing the concept of "optimal polynomial-time estimators." We prove some existence theorems and completeness results, and show that optimal polynomial-time estimators exhibit many parallels with "classical" probability theory. |
| title | Optimal Polynomial-Time Estimators: A Bayesian Notion of Approximation Algorithm |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/1608.04112 |