Multifold Confidence Intervals in Collaborative Mean Estimation (ColME) Using Sample Statistics

TL;DR

This paper develops a collaborative mean estimation framework that uses sample statistics to construct multifold confidence intervals, enabling personalized online learning in heterogeneous environments with real-time variance and kurtosis estimation.

Contribution

It introduces a unified method for constructing confidence intervals based on sample mean, variance, and kurtosis, improving collaborative estimation in diverse data distributions.

Findings

Enhanced accuracy in mean estimation through multifold confidence intervals.

Real-time variance and kurtosis estimation improves adaptability.

Framework handles complex distribution similarities and differences.

Abstract

The rapid growth of digital devices and IoT has intensified the demand for collaborative learning. Since these devices generate sensitive and high-dimensional data, centralized transmission is often impractical, while local learning suffers from slow convergence. Collaborative approaches can alleviate these issues by allowing agents to use information from one another to improve estimation. Each agent faces a personalized learning problem, and collaboration is beneficial among agents whose data are generated from the same distributions. This paper studies the problem of personalized online mean estimation in heterogeneous environments, where each agent observes data from its own sigma-sub-Gaussian distribution. Collaborative algorithms enable agents to identify similarity classes in real time and exploit information from agents belonging to the the same class to improve convergence and accuracy. The work builds on existing approaches: the collaborative mean estimation (colME) and its graph-based extensions (C-colME and B-colME), which improve scalability and robustness. Since the variance estimation plays a crucial role in the above mentioned algorithms, a method for accurate, local and real-time estimation of variance is proposed. Estimation of sample kurtosis is also incorporated. We derive the CI estimators for the sample standard deviation and sample kurtosis. These results are combined with sample colME methods to design a unified procedure for constructing multifold CI based jointly on the sample mean, sample variance, and sample kurtosis. This framework enables colME in challenging scenarios, such as when classes share similar means but differ in variances, or when both means and variances are alike while the underlying distributions diverge in higher-order characteristics.