### Abstract

In the rejection sampling problem, a sequence of samples distributed according to Q are observed sequentially by a sampler which stops and makes the selection at a certain point so that the selected sample is distributed according to P. Harsha-Jain-McAllester-Radhakrishnan showed that the expected length of a variable-length compression of the index of the selected sample is approximately D(PVert Q). We prove Renyi generalizations of their result under some regularity conditions on the information spectrum. It turns out that causality matters except for Renyi divergence of order 1. For alphain(0,1), the minimum alpha -moment of the selected index is approximately exp left(alpha D- frac 1 1-alpha(PVert Q)right) · In contrast, in the variant where the sequence is observed noncausally, the minimum alpha -moment ((alphageq 0) is approximately exp(alpha D- 1+alpha(PVert Q)). The proof is based on a simple optimization duality between sampling and covering.

Original language | English (US) |
---|---|

Title of host publication | 2018 IEEE International Symposium on Information Theory, ISIT 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1565-1569 |

Number of pages | 5 |

ISBN (Print) | 9781538647806 |

DOIs | |

State | Published - Aug 15 2018 |

Event | 2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States Duration: Jun 17 2018 → Jun 22 2018 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
---|---|

Volume | 2018-June |

ISSN (Print) | 2157-8095 |

### Other

Other | 2018 IEEE International Symposium on Information Theory, ISIT 2018 |
---|---|

Country | United States |

City | Vail |

Period | 6/17/18 → 6/22/18 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Rejection Sampling and Noncausal Sampling under Moment Constraints'. Together they form a unique fingerprint.

## Cite this

*2018 IEEE International Symposium on Information Theory, ISIT 2018*(pp. 1565-1569). [8437857] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2018.8437857