A Biased Estimator for MinMax Sampling and Distributed Aggregation

TL;DR

This paper introduces B-MinMax, a biased estimator for MinMax sampling that reduces variance and mean squared error, especially effective in distributed data aggregation with small sample sizes.

Contribution

The paper proposes B-MinMax, a biased estimation method that improves variance reduction over traditional MinMax sampling in distributed data aggregation.

Findings

B-MinMax achieves lower MSE than unbiased MinMax.

B-MinMax is preferable for small sample sizes and limited aggregation.

Experiments demonstrate substantial MSE reduction in practical scenarios.

Abstract

MinMax sampling is a technique for downsampling a real-valued vector which minimizes the maximum variance over all vector components. This approach is useful for reducing the amount of data that must be sent over a constrained network link (e.g. in the wide-area). MinMax can provide unbiased estimates of the vector elements, along with unbiased estimates of aggregates when vectors are combined from multiple locations. In this work, we propose a biased MinMax estimation scheme, B-MinMax, which trades an increase in estimator bias for a reduction in variance. We prove that when no aggregation is performed, B-MinMax obtains a strictly lower MSE compared to the unbiased MinMax estimator. When aggregation is required, B-MinMax is preferable when sample sizes are small or the number of aggregated vectors is limited. Our experiments show that this approach can substantially reduce the MSE for MinMax sampling in many practical settings.