Universal Behavior in Large-scale Aggregation of Independent Noisy Observations

TL;DR

This paper investigates how large-scale aggregation of noisy data behaves, revealing universal scaling laws and conditions under which lossy compression outperforms lossless methods, especially at high noise levels.

Contribution

It introduces a universal framework for understanding the tradeoffs in aggregating noisy observations, including a scaling relation and the critical noise threshold for lossy versus lossless aggregation.

Findings

Large-scale lossy aggregation can outperform lossless aggregation at high noise levels.

A universal scaling relation links collective error to system capacity.

Critical noise level determines when lossy aggregation becomes advantageous.

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 protypical 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 which are independent of system capacity can be obtained by considering asymptotic behavior when the system capacity increases toward infinity.