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Due to the falling costs of data acquisition and storage, researchers and industry analysts often want to find all instances of rare events in large datasets. For instance, scientists can cheaply capture thousands of hours of video, but are limited by the need to manually inspect long videos to identify relevant objects and events. To reduce this cost, recent work proposes to use cheap proxy models, such as image classifiers, to identify an approximate set of data points satisfying a data selection filter. Unfortunately, this recent work does not provide the statistical accuracy guarantees necessary in scientific and production settings. In this work, we introduce novel algorithms for approximate selection queries with statistical accuracy guarantees. Namely, given a limited number of exact identifications from an oracle, often a human or an expensive machine learning model, our algorithms meet a minimum precision or recall target with high probability. In contrast, existing approaches can catastrophically fail in satisfying these recall and precision targets. We show that our algorithms can improve query result quality by up to 30 x for both the precision and recall targets in both real and synthetic datasets.

Interactive analytics increasingly involves querying for quantiles over sub-populations of high cardinality datasets. Data processing engines such as Druid and Spark use mergeable summaries to estimate quantiles, but summary merge times can be a bottleneck during 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 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 shows that the moments sketch can achieve less than 1 percent quantile error with 15× less overhead than comparable summaries, improving end query time in the MacroBase engine by up to 7× and the Druid engine by up to 60×. *

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