### Abstract

Hypothesis testing of covariance matrices is an important problem in multivariate analysis. Given n data samples and a covariance matrix Σ0, the goal is to determine whether or not the data is consistent with this matrix. In this paper we introduce a framework that we call sketched covariance testing, where the data is provided after being compressed by multiplying by a 'sketching' matrix A chosen by the analyst. We propose a statistical test in this setting and quantify an achievable sample complexity as a function of the amount of compression. Our result reveals an intriguing achievable tradeoff between the compression ratio and the statistical information required for reliable hypothesis testing; the sample complexity increases as the fourth power of the amount of compression.

Original language | English (US) |
---|---|

Title of host publication | 2017 IEEE International Symposium on Information Theory, ISIT 2017 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 2268-2272 |

Number of pages | 5 |

ISBN (Electronic) | 9781509040964 |

DOIs | |

State | Published - Aug 9 2017 |

Externally published | Yes |

Event | 2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany Duration: Jun 25 2017 → Jun 30 2017 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
---|---|

ISSN (Print) | 2157-8095 |

### Other

Other | 2017 IEEE International Symposium on Information Theory, ISIT 2017 |
---|---|

Country | Germany |

City | Aachen |

Period | 6/25/17 → 6/30/17 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

### Cite this

*2017 IEEE International Symposium on Information Theory, ISIT 2017*(pp. 2268-2272). [8006933] (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2017.8006933

**Sketched covariance testing : A compression-statistics tradeoff.** / Dasarathy, Gautam; Shah, Parikshit; Baraniuk, Richard G.

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

*2017 IEEE International Symposium on Information Theory, ISIT 2017.*, 8006933, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 2268-2272, 2017 IEEE International Symposium on Information Theory, ISIT 2017, Aachen, Germany, 6/25/17. https://doi.org/10.1109/ISIT.2017.8006933

}

TY - GEN

T1 - Sketched covariance testing

T2 - A compression-statistics tradeoff

AU - Dasarathy, Gautam

AU - Shah, Parikshit

AU - Baraniuk, Richard G.

PY - 2017/8/9

Y1 - 2017/8/9

N2 - Hypothesis testing of covariance matrices is an important problem in multivariate analysis. Given n data samples and a covariance matrix Σ0, the goal is to determine whether or not the data is consistent with this matrix. In this paper we introduce a framework that we call sketched covariance testing, where the data is provided after being compressed by multiplying by a 'sketching' matrix A chosen by the analyst. We propose a statistical test in this setting and quantify an achievable sample complexity as a function of the amount of compression. Our result reveals an intriguing achievable tradeoff between the compression ratio and the statistical information required for reliable hypothesis testing; the sample complexity increases as the fourth power of the amount of compression.

AB - Hypothesis testing of covariance matrices is an important problem in multivariate analysis. Given n data samples and a covariance matrix Σ0, the goal is to determine whether or not the data is consistent with this matrix. In this paper we introduce a framework that we call sketched covariance testing, where the data is provided after being compressed by multiplying by a 'sketching' matrix A chosen by the analyst. We propose a statistical test in this setting and quantify an achievable sample complexity as a function of the amount of compression. Our result reveals an intriguing achievable tradeoff between the compression ratio and the statistical information required for reliable hypothesis testing; the sample complexity increases as the fourth power of the amount of compression.

UR - http://www.scopus.com/inward/record.url?scp=85034039775&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85034039775&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2017.8006933

DO - 10.1109/ISIT.2017.8006933

M3 - Conference contribution

AN - SCOPUS:85034039775

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2268

EP - 2272

BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017

PB - Institute of Electrical and Electronics Engineers Inc.

ER -