# Proof: Accelerating Approximate Aggregation Queries with Expensive Predicates

arXiv: https://arxiv.org/abs/2107.12525 · HTML: https://mlsanity.com/paper/2107.12525/

## Key facts

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- First posted on arXiv 27 Jul 2021.

## Abstract (arXiv)

Given a dataset D, we are interested in computing the mean of a subset of D which matches a predicate. ABae leverages stratified sampling and proxy models to efficiently compute this statistic given a sampling budget N. In this document, we theoretically analyze ABae and show that the MSE of the estimate decays at rate O(N1-1 + N2-1 + N11/2N2-3/2), where N=K · N1+N2 for some integer constant K and K · N1 and N2 represent the number of samples used in Stage 1 and Stage 2 of ABae respectively. Hence, if a constant fraction of the total sample budget N is allocated to each stage, we will achieve a mean squared error of O(N-1) which matches the rate of mean squared error of the optimal stratified sampling algorithm given a priori knowledge of the predicate positive rate and standard deviation per stratum.