## Abstract

We propose a new active learning algorithm for parametric linear regression with random design. We provide finite sample convergence guarantees for general distributions in the misspecified model. This is the first active learner for this setting that provably can improve over passive learning. Unlike other learning settings (such as classification), in regression the passive learning rate of O(1/ε) cannot in general be improved upon. Nonetheless, the so-called 'constant' in the rate of convergence, which is characterized by a distribution-dependent risk, can be improved in many cases. For a given distribution, achieving the optimal risk requires prior knowledge of the distribution. Following the stratification technique advocated in Monte-Carlo function integration, our active learner approaches the optimal risk using piecewise constant approximations.

Original language | English GB |
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Title of host publication | Advances in Neural Information Processing Systems 27 (NIPS 2014) |

Pages | 469-477 |

Number of pages | 9 |

Volume | 1 |

Edition | January |

State | Published - 2014 |

Event | 28th Annual Conference on Neural Information Processing Systems 2014, NIPS 2014 - Montreal, Canada Duration: 8 Dec 2014 → 13 Dec 2014 |

### Conference

Conference | 28th Annual Conference on Neural Information Processing Systems 2014, NIPS 2014 |
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Country/Territory | Canada |

City | Montreal |

Period | 8/12/14 → 13/12/14 |

## ASJC Scopus subject areas

- Computer Networks and Communications
- Information Systems
- Signal Processing