Moment-Based Quantile Sketches for Efficient High Cardinality Aggregation Queries
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Interactive analytics increasingly involves querying for quantiles over specific sub-populations and time windows of high cardinality datasets. Data processing engines such as Druid and Spark use mergeable summaries to estimate quantiles on these large datasets, but summary merge times are a bottleneck during high-cardinality aggregation. We show how a compact and efficiently mergeable quantile sketch can support aggregation workloads. This data structure, which we refer to as the moments sketch, operates with a small memory footprint (200 bytes) and computationally efficient (50ns) merges by tracking only a set of summary statistics, notably the sample moments. We demonstrate how we can efficiently and practically estimate quantiles using the method of moments and the maximum entropy principle, and show how the use of a cascade further improves query time for threshold predicates. Empirical evaluation on real-world datasets shows that the moments sketch can achieve less than 1 percent error with 40 times less merge overhead than comparable summaries, improving end query time in the MacroBase engine by up to 7 times and the Druid engine by up to 60 times.
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