### Abstract

We consider the CEO problem for belief sharing. Multiple subordinates observe independently corrupted versions of uniformly distributed data and transmit coded versions over rate-limited links to a CEO who then estimates the underlying data. Agents are not allowed to convene before transmitting their observations. This formulation is motivated by the practical problem of a firm's CEO estimating uniformly distributed beliefs about a sequence of events, before acting on them. Agents' observations are modeled as jointly distributed with the underlying data through a given conditional probability density function. We study the asymptotic behavior of the minimum achievable mean squared error distortion at the CEO in the limit when the number of agents L and the sum rate R tend to infinity. We establish a 1/R^{2} convergence of the distortion, an intermediate regime of performance between the exponential behavior in discrete CEO problems [Berger, Zhang, and Viswanathan (1996)], and the 1/R behavior in Gaussian CEO problems [Viswanathan and Berger (1997)]. Achievability is proved by a layered architecture with scalar quantization, distributed entropy coding, and midrange estimation. The converse is proved using the Bayesian Chazan-Zakai-Ziv bound.

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

Title of host publication | 2015 IEEE Information Theory Workshop, ITW 2015 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

ISBN (Electronic) | 9781479955268 |

DOIs | |

State | Published - Jun 24 2015 |

Event | 2015 IEEE Information Theory Workshop, ITW 2015 - Jerusalem, Israel Duration: Apr 26 2015 → May 1 2015 |

### Publication series

Name | 2015 IEEE Information Theory Workshop, ITW 2015 |
---|

### Other

Other | 2015 IEEE Information Theory Workshop, ITW 2015 |
---|---|

Country | Israel |

City | Jerusalem |

Period | 4/26/15 → 5/1/15 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Computer Networks and Communications
- Information Systems
- Computational Theory and Mathematics

### Cite this

*2015 IEEE Information Theory Workshop, ITW 2015*[7133076] (2015 IEEE Information Theory Workshop, ITW 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ITW.2015.7133076

**CEO problem for belief sharing.** / Vempaty, Aditya; Varshney, Lav R.

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

*2015 IEEE Information Theory Workshop, ITW 2015.*, 7133076, 2015 IEEE Information Theory Workshop, ITW 2015, Institute of Electrical and Electronics Engineers Inc., 2015 IEEE Information Theory Workshop, ITW 2015, Jerusalem, Israel, 4/26/15. https://doi.org/10.1109/ITW.2015.7133076

}

TY - GEN

T1 - CEO problem for belief sharing

AU - Vempaty, Aditya

AU - Varshney, Lav R

PY - 2015/6/24

Y1 - 2015/6/24

N2 - We consider the CEO problem for belief sharing. Multiple subordinates observe independently corrupted versions of uniformly distributed data and transmit coded versions over rate-limited links to a CEO who then estimates the underlying data. Agents are not allowed to convene before transmitting their observations. This formulation is motivated by the practical problem of a firm's CEO estimating uniformly distributed beliefs about a sequence of events, before acting on them. Agents' observations are modeled as jointly distributed with the underlying data through a given conditional probability density function. We study the asymptotic behavior of the minimum achievable mean squared error distortion at the CEO in the limit when the number of agents L and the sum rate R tend to infinity. We establish a 1/R2 convergence of the distortion, an intermediate regime of performance between the exponential behavior in discrete CEO problems [Berger, Zhang, and Viswanathan (1996)], and the 1/R behavior in Gaussian CEO problems [Viswanathan and Berger (1997)]. Achievability is proved by a layered architecture with scalar quantization, distributed entropy coding, and midrange estimation. The converse is proved using the Bayesian Chazan-Zakai-Ziv bound.

AB - We consider the CEO problem for belief sharing. Multiple subordinates observe independently corrupted versions of uniformly distributed data and transmit coded versions over rate-limited links to a CEO who then estimates the underlying data. Agents are not allowed to convene before transmitting their observations. This formulation is motivated by the practical problem of a firm's CEO estimating uniformly distributed beliefs about a sequence of events, before acting on them. Agents' observations are modeled as jointly distributed with the underlying data through a given conditional probability density function. We study the asymptotic behavior of the minimum achievable mean squared error distortion at the CEO in the limit when the number of agents L and the sum rate R tend to infinity. We establish a 1/R2 convergence of the distortion, an intermediate regime of performance between the exponential behavior in discrete CEO problems [Berger, Zhang, and Viswanathan (1996)], and the 1/R behavior in Gaussian CEO problems [Viswanathan and Berger (1997)]. Achievability is proved by a layered architecture with scalar quantization, distributed entropy coding, and midrange estimation. The converse is proved using the Bayesian Chazan-Zakai-Ziv bound.

UR - http://www.scopus.com/inward/record.url?scp=84938909219&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84938909219&partnerID=8YFLogxK

U2 - 10.1109/ITW.2015.7133076

DO - 10.1109/ITW.2015.7133076

M3 - Conference contribution

AN - SCOPUS:84938909219

T3 - 2015 IEEE Information Theory Workshop, ITW 2015

BT - 2015 IEEE Information Theory Workshop, ITW 2015

PB - Institute of Electrical and Electronics Engineers Inc.

ER -