Exact PPS Sampling with Bounded Sample Size

TL;DR

This paper introduces a new PPS sampling method that guarantees a fixed maximum sample size while maintaining the probability proportional to size property, improving control over sample size and processing efficiency.

Contribution

The paper presents a novel PPS sampling scheme that enforces the PPS property with a bounded sample size, balancing accuracy and resource constraints.

Findings

Ensures sample size never exceeds target n

Maintains PPS property at all times

Operates with O(1) amortized processing time per item

Abstract

Probability proportional to size (PPS) sampling schemes with a target sample size aim to produce a sample comprising a specified number $n$ of items while ensuring that each item in the population appears in the sample with a probability proportional to its specified "weight" (also called its "size"). These two objectives, however, cannot always be achieved simultaneously. Existing PPS schemes prioritize control of the sample size, violating the PPS property if necessary. We provide a new PPS scheme that allows a different trade-off: our method enforces the PPS property at all times while ensuring that the sample size never exceeds the target value $n$. The sample size is exactly equal to $n$ if possible, and otherwise has maximal expected value and minimal variance. Thus we bound the sample size, thereby avoiding storage overflows and helping to control the time required for analytics over the sample, while allowing the user complete control over the sample contents. The method is both simple to implement and efficient, being a one-pass streaming algorithm with an amortized processing time of $O(1)$ per item.