On the Statistical Complexity of Sample Amplification
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929502373806080 |
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| author | Axelrod, Brian Garg, Shivam Han, Yanjun Sharan, Vatsal Valiant, Gregory |
| author_facet | Axelrod, Brian Garg, Shivam Han, Yanjun Sharan, Vatsal Valiant, Gregory |
| contents | The ``sample amplification'' problem formalizes the following question: Given $n$ i.i.d. samples drawn from an unknown distribution $P$, when is it possible to produce a larger set of $n+m$ samples which cannot be distinguished from $n+m$ i.i.d. samples drawn from $P$? In this work, we provide a firm statistical foundation for this problem by deriving generally applicable amplification procedures, lower bound techniques and connections to existing statistical notions. Our techniques apply to a large class of distributions including the exponential family, and establish a rigorous connection between sample amplification and distribution learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_04315 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Statistical Complexity of Sample Amplification Axelrod, Brian Garg, Shivam Han, Yanjun Sharan, Vatsal Valiant, Gregory Statistics Theory Data Structures and Algorithms Information Theory Machine Learning The ``sample amplification'' problem formalizes the following question: Given $n$ i.i.d. samples drawn from an unknown distribution $P$, when is it possible to produce a larger set of $n+m$ samples which cannot be distinguished from $n+m$ i.i.d. samples drawn from $P$? In this work, we provide a firm statistical foundation for this problem by deriving generally applicable amplification procedures, lower bound techniques and connections to existing statistical notions. Our techniques apply to a large class of distributions including the exponential family, and establish a rigorous connection between sample amplification and distribution learning. |
| title | On the Statistical Complexity of Sample Amplification |
| topic | Statistics Theory Data Structures and Algorithms Information Theory Machine Learning |
| url | https://arxiv.org/abs/2201.04315 |