Fundamental limits for weighted empirical approximations of tilted distributions
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arXiv
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| Auteurs principaux: | , , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909978173898752 |
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| author | Iyer, Sarvesh Ravichandran Mandal, Himadri Gupta, Dhruman Gupta, Rushil Bandhyopadhyay, Agniv Bassamboo, Achal Gupta, Varun Juneja, Sandeep |
| author_facet | Iyer, Sarvesh Ravichandran Mandal, Himadri Gupta, Dhruman Gupta, Rushil Bandhyopadhyay, Agniv Bassamboo, Achal Gupta, Varun Juneja, Sandeep |
| contents | Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in rare event simulation. In this article, we discuss the asymptotic efficiency of a self-normalized importance sampler of the tilted distribution. We provide a sharp characterization of its accuracy, given the number of samples and the degree of tilt. Our findings reveal a surprising dichotomy: while the number of samples needed to accurately tilt a bounded random vector increases polynomially in the tilt amount, it increases at a super polynomial rate for unbounded distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23979 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fundamental limits for weighted empirical approximations of tilted distributions Iyer, Sarvesh Ravichandran Mandal, Himadri Gupta, Dhruman Gupta, Rushil Bandhyopadhyay, Agniv Bassamboo, Achal Gupta, Varun Juneja, Sandeep Statistics Theory Machine Learning Probability 62D05 G.3 Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in rare event simulation. In this article, we discuss the asymptotic efficiency of a self-normalized importance sampler of the tilted distribution. We provide a sharp characterization of its accuracy, given the number of samples and the degree of tilt. Our findings reveal a surprising dichotomy: while the number of samples needed to accurately tilt a bounded random vector increases polynomially in the tilt amount, it increases at a super polynomial rate for unbounded distributions. |
| title | Fundamental limits for weighted empirical approximations of tilted distributions |
| topic | Statistics Theory Machine Learning Probability 62D05 G.3 |
| url | https://arxiv.org/abs/2512.23979 |