### Abstract

Original language | English |
---|---|

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 |
---|---|

Country | Singapore |

City | Singapore |

Period | 16/11/94 → 18/11/94 |

### Fingerprint

### Bibliographical note

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

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

### Cite this

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

}

*Advances in Neural Information Processing Systems 9.*vol. 9, Proceeding of the 1996 conference, MIT, pp. 347-353, Advances in Neural Information Processing Systems 1994, Singapore, Singapore, 16/11/94.

**Regression with input-dependent noise: A Bayesian treatment.** / Bishop, Christopher M.; Qazaz, Cazhaow S.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Regression with input-dependent noise: A Bayesian treatment

AU - Bishop, Christopher M.

AU - Qazaz, Cazhaow S.

N1 - Copyright of the Massachusetts Institute of Technology Press (MIT Press)

PY - 1997/5

Y1 - 1997/5

N2 - 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.

AB - 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.

KW - regression problem

KW - target data

KW - Gaussian noise

KW - error function

KW - noise variance

UR - http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=3990

M3 - Chapter

SN - 0262100657

VL - 9

T3 - Proceeding of the 1996 conference

SP - 347

EP - 353

BT - Advances in Neural Information Processing Systems 9

A2 - Mozer, Michael C.

A2 - Jordan, Michael I.

A2 - Petsche, Thomas

PB - MIT

ER -