### Abstract

A guiding principle for data reduction in statistical inference is the sufficiency principle. This paper extends the classical sufficiency principle to decentralized inference, i.e., data reduction needs to be achieved in a decentralized manner. We examine the notions of local and global sufficient statistics and the relationship between the two for decentralized inference under different observation models. We then consider the impact of quantization on decentralized data reduction, which is often needed when communications among sensors are subject to finite capacity constraints. The central question we intend to ask is: if each node in a decentralized inference system has to summarize its data using a finite number of bits, is it still optimal to implement data reduction using global sufficient statistics prior to quantization? We show that the answer is negative using a simple example and proceed to identify conditions under which sufficiency based data reduction followed by quantization is indeed optimal. They include the well known case when the data at decentralized nodes are conditionally independent as well as a class of problems with conditionally dependent observations that admit conditional independence structure through the introduction of an appropriately chosen hidden variable.

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

Article number | 6728713 |

Pages (from-to) | 1775-1784 |

Number of pages | 10 |

Journal | IEEE Transactions on Signal Processing |

Volume | 62 |

Issue number | 7 |

DOIs | |

State | Published - Apr 1 2014 |

### Fingerprint

### Keywords

- Decentralized inference
- quantization
- sufficiency principle
- sufficient statistic

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Signal Processing

### Cite this

*IEEE Transactions on Signal Processing*,

*62*(7), 1775-1784. [6728713]. https://doi.org/10.1109/TSP.2014.2303432

**Decentralized data reduction with quantization constraints.** / Xu, Ge; Zhu, Shengyu; Chen, Biao.

Research output: Contribution to journal › Article

*IEEE Transactions on Signal Processing*, vol. 62, no. 7, 6728713, pp. 1775-1784. https://doi.org/10.1109/TSP.2014.2303432

}

TY - JOUR

T1 - Decentralized data reduction with quantization constraints

AU - Xu, Ge

AU - Zhu, Shengyu

AU - Chen, Biao

PY - 2014/4/1

Y1 - 2014/4/1

N2 - A guiding principle for data reduction in statistical inference is the sufficiency principle. This paper extends the classical sufficiency principle to decentralized inference, i.e., data reduction needs to be achieved in a decentralized manner. We examine the notions of local and global sufficient statistics and the relationship between the two for decentralized inference under different observation models. We then consider the impact of quantization on decentralized data reduction, which is often needed when communications among sensors are subject to finite capacity constraints. The central question we intend to ask is: if each node in a decentralized inference system has to summarize its data using a finite number of bits, is it still optimal to implement data reduction using global sufficient statistics prior to quantization? We show that the answer is negative using a simple example and proceed to identify conditions under which sufficiency based data reduction followed by quantization is indeed optimal. They include the well known case when the data at decentralized nodes are conditionally independent as well as a class of problems with conditionally dependent observations that admit conditional independence structure through the introduction of an appropriately chosen hidden variable.

AB - A guiding principle for data reduction in statistical inference is the sufficiency principle. This paper extends the classical sufficiency principle to decentralized inference, i.e., data reduction needs to be achieved in a decentralized manner. We examine the notions of local and global sufficient statistics and the relationship between the two for decentralized inference under different observation models. We then consider the impact of quantization on decentralized data reduction, which is often needed when communications among sensors are subject to finite capacity constraints. The central question we intend to ask is: if each node in a decentralized inference system has to summarize its data using a finite number of bits, is it still optimal to implement data reduction using global sufficient statistics prior to quantization? We show that the answer is negative using a simple example and proceed to identify conditions under which sufficiency based data reduction followed by quantization is indeed optimal. They include the well known case when the data at decentralized nodes are conditionally independent as well as a class of problems with conditionally dependent observations that admit conditional independence structure through the introduction of an appropriately chosen hidden variable.

KW - Decentralized inference

KW - quantization

KW - sufficiency principle

KW - sufficient statistic

UR - http://www.scopus.com/inward/record.url?scp=84897911777&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84897911777&partnerID=8YFLogxK

U2 - 10.1109/TSP.2014.2303432

DO - 10.1109/TSP.2014.2303432

M3 - Article

AN - SCOPUS:84897911777

VL - 62

SP - 1775

EP - 1784

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 7

M1 - 6728713

ER -