### Abstract

The following detection problem is studied, in which there are M sequences of samples out of which one outlier sequence needs to be detected. Each typical sequence contains n independent and identically distributed (i.i.d.) continuous observations from a known distribution π, and the outlier sequence contains n i.i.d. observations from an outlier distribution μ, which is distinct from n, but otherwise unknown. A universal test based on Kullback-Leibler (KL) divergence is built to approximate the maximum likelihood test, with known π and unknown μ. A KL divergence estimator based on data-dependent partitions is employed, and is shown to converge to its true value exponentially fast when the density ratio satisfies 0 <Kl ≤ dμ/dπ ≤ K2, where K1 and K2 are positive constants. The performance of such a KL divergence estimator further implies that the outlier detection test is exponentially consistent. The detection performance of the KL divergence based test is compared with that of a recently introduced test for this problem based on the machine learning approach of maximum mean discrepancy (MMD). Regimes in which the KL divergence based test is better than the MMD based test are identified.

Original language | English (US) |
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Title of host publication | 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 4254-4258 |

Number of pages | 5 |

Volume | 2016-May |

ISBN (Electronic) | 9781479999880 |

DOIs | |

State | Published - May 18 2016 |

Event | 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China Duration: Mar 20 2016 → Mar 25 2016 |

### Other

Other | 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 |
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Country | China |

City | Shanghai |

Period | 3/20/16 → 3/25/16 |

### Keywords

- Kullback-Leibler divergence
- maximum mean discrepancy
- outlier hypothesis testing
- universal exponential consistency

### ASJC Scopus subject areas

- Signal Processing
- Software
- Electrical and Electronic Engineering

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## Cite this

*2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings*(Vol. 2016-May, pp. 4254-4258). [7472479] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2016.7472479