### Abstract

In most treatments of the regression problem it is assumed that the distribution of target data can be described by a deterministic function of the inputs, together with additive Gaussian noise having constant variance. The use of maximum likelihood to train such models then corresponds to the minimization of a sum-of-squares error function. In many applications a more realistic model would allow the noise variance itself to depend on the input variables. However, the use of maximum likelihood to train such models would give highly biased results. In this paper we show how a Bayesian treatment can allow for an input-dependent variance while overcoming the bias of maximum likelihood.

Original language | English |
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Title of host publication | Advances in Neural Information Processing Systems 9 |

Editors | Michael C. Mozer, Michael I. Jordan, Thomas Petsche |

Publisher | MIT |

Pages | 347-353 |

Number of pages | 7 |

Volume | 9 |

ISBN (Print) | 0262100657 |

Publication status | Published - May 1997 |

Event | Advances in Neural Information Processing Systems 1994 - Singapore, Singapore Duration: 16 Nov 1994 → 18 Nov 1994 |

### Publication series

Name | Proceeding of the 1996 conference |
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Publisher | Massachusetts Institute of Technology Press (MIT Press) |

### Other

Other | Advances in Neural Information Processing Systems 1994 |
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Country | Singapore |

City | Singapore |

Period | 16/11/94 → 18/11/94 |

### Bibliographical note

Copyright of the Massachusetts Institute of Technology Press (MIT Press)### Keywords

- regression problem
- target data
- Gaussian noise
- error function
- noise variance

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## Cite this

Bishop, C. M., & Qazaz, C. S. (1997). Regression with input-dependent noise: A Bayesian treatment. In M. C. Mozer, M. I. Jordan, & T. Petsche (Eds.),

*Advances in Neural Information Processing Systems 9*(Vol. 9, pp. 347-353). (Proceeding of the 1996 conference). MIT.