Universal behavior in large-scale aggregation of independent noisy observations

NTT Communication Science Laboratories, NTT Corporation - Kyoto 619-0237, Japan

Corresponding author: murayama@cslab.kecl.ntt.co.jp

Received: 21 May 2009
Accepted: 31 July 2009

Abstract

Aggregation of noisy observations involves a difficult tradeoff between observation quality, which can be increased by increasing the number of observations, and aggregation quality which decreases if the number of observations is too large. We clarify this behavior for a prototypical system in which arbitrarily large numbers of observations exceeding the system capacity can be aggregated using lossy data compression. We show the existence of a scaling relation between the collective error and the system capacity, and show that large-scale lossy aggregation can outperform lossless aggregation above a critical level of observation noise. Further, we show that universal results for scaling and critical value of noise can be obtained when the system capacity increases toward infinity.