## Abstract

We start by demonstrating that an elementary learning task—learning a linear filter

from training data by means of regression—can be solved very efficiently for feature

spaces of very high dimensionality. In a second step, firstly, acknowledging that such

high-dimensional learning tasks typically benefit from some form of regularization and,

secondly, arguing that the problem of scale has not been taken care of in a very satis-

factory manner, we come to a combined resolution of both of these shortcomings by

proposing a technique that we coin scale regularization. This regularization problem can

also be solved relatively efficient. All in all, the idea is to properly control the scale of a

trained filter, which we solve by introducing a specific regularization term into the overall

objective function. We demonstrate, on an artificial filter learning problem, the capabil-

ities of our basic filter. In particular, we demonstrate that it clearly outperforms the de

facto standard Tikhonov regularization, which is the one employed in ridge regression or

Wiener filtering.

from training data by means of regression—can be solved very efficiently for feature

spaces of very high dimensionality. In a second step, firstly, acknowledging that such

high-dimensional learning tasks typically benefit from some form of regularization and,

secondly, arguing that the problem of scale has not been taken care of in a very satis-

factory manner, we come to a combined resolution of both of these shortcomings by

proposing a technique that we coin scale regularization. This regularization problem can

also be solved relatively efficient. All in all, the idea is to properly control the scale of a

trained filter, which we solve by introducing a specific regularization term into the overall

objective function. We demonstrate, on an artificial filter learning problem, the capabil-

ities of our basic filter. In particular, we demonstrate that it clearly outperforms the de

facto standard Tikhonov regularization, which is the one employed in ridge regression or

Wiener filtering.

Originalsprog | Engelsk |
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Titel | Proceedings of BMVC 2017 |

Antal sider | 12 |

Forlag | British Machine Vision Conference |

Publikationsdato | jul. 2017 |

Status | Udgivet - jul. 2017 |

Begivenhed | British Machine Vision Conference 2017 - Imperial College London, London, Storbritannien Varighed: 4 sep. 2017 → 7 sep. 2017 https://bmvc2017.london/ |

### Konference

Konference | British Machine Vision Conference 2017 |
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Lokation | Imperial College London |

Land/Område | Storbritannien |

By | London |

Periode | 04/09/2017 → 07/09/2017 |

Internetadresse |