### Abstract

We study the problems of data compression, gambling and prediction of a sequence x^{n} = x_{1}x_{2}...x_{n} from an alphabet X, in terms of regret with respect to various families of probability distributions. It is known that the regret of the Bayes mixture with respect to a general exponential families asymptotically achieves the minimax value when variants of Jeffreys prior are used, under the condition that the maximum likelihood estimate is in the interior of the parameter space. We discuss a modification of Jeffreys prior which has measure outside the given family of densities, to achieve minimax regret with respect to non-exponential type families, e.g. curved exponential families and mixture families. These results also provide characterization of Rissanen's stochastic complexity for those classes.

Original language | English |
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Title of host publication | 2013 IEEE Information Theory Workshop, ITW 2013 |

DOIs | |

Publication status | Published - Dec 1 2013 |

Event | 2013 IEEE Information Theory Workshop, ITW 2013 - Seville, Spain Duration: Sep 9 2013 → Sep 13 2013 |

### Publication series

Name | 2013 IEEE Information Theory Workshop, ITW 2013 |
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### Other

Other | 2013 IEEE Information Theory Workshop, ITW 2013 |
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Country | Spain |

City | Seville |

Period | 9/9/13 → 9/13/13 |

### All Science Journal Classification (ASJC) codes

- Information Systems

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## Cite this

*2013 IEEE Information Theory Workshop, ITW 2013*[6691254] (2013 IEEE Information Theory Workshop, ITW 2013). https://doi.org/10.1109/ITW.2013.6691254