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Random sampling is an essential tool in the processing and transmission ofdata. It is used to summarize data too large to store or manipulate and meetresource constraints on bandwidth or battery power. Estimators that are appliedto the sample facilitate fast approximate processing of queries posed over theoriginal data and the value of the sample hinges on the quality of theseestimators.  Our work targets data sets such as request and traffic logs and sensormeasurements, where data is repeatedly collected over multiple {\em instances}:time periods, locations, or snapshots.  We are interested in queries that span multiple instances, such as distinctcounts and distance measures over selected records. These queries are used forapplications ranging from planning to anomaly and change detection.  Unbiased low-variance estimators are particularly effective as the relativeerror decreases with the number of selected record keys.  The Horvitz-Thompson estimator, known to minimize variance for sampling with"all or nothing" outcomes (which reveals exacts value or no information onestimated quantity), is not optimal for multi-instance operations for which anoutcome may provide partial information.  We present a general principled methodology for the derivation of (Pareto)optimal unbiased estimators over sampled instances and aim to understand itspotential. We demonstrate significant improvement in estimate accuracy offundamental queries for common sampling schemes.

Get the Most out of Your Sample: Optimal Unbiased Estimators using Partial Information