Ming-Hung Shih | Searcharxiv

arXiv2019

Random Sampling for Group-By Queries

Random sampling has been widely used in approximate query processing on large databases, due to its potential to significantly reduce resource usage and response times, at the cost of a small approximation error. We consider random sampling for answering the ubiquitous class of group-by queries, which first group data according to one or more attributes, and then aggregate within each group after filtering through a predicate. The challenge with group-by queries is that a sampling method cannot focus on optimizing the quality of a single answer (e.g. the mean of selected data), but must simultaneously optimize the quality of a set of answers (one per group). We present CVOPT, a query- and data-driven sampling framework for a set of group-by queries. To evaluate the quality of a sample, CVOPT defines a metric based on the norm (e.g. $\ell_2$ or $\ell_\infty$) of the coefficients of variation (CVs) of different answers, and constructs a stratified sample that provably optimizes the metric. CVOPT can handle group-by queries on data where groups have vastly different statistical characteristics, such as frequencies, means, or variances. CVOPT jointly optimizes for multiple aggregations and multiple group-by clauses, and provides a way to prioritize specific groups or aggregates. It can be tuned to cases when partial information about a query workload is known, such as a data warehouse where queries are scheduled to run periodically. Our experimental results show that CVOPT outperforms current state-of-the-art on sample quality and estimation accuracy for group-by queries. On a set of queries on two real-world data sets, CVOPT yields relative errors that are 5x smaller than competing approaches, under the same space budget.

cs.DB↗

arXiv2018

Variance-Optimal Offline and Streaming Stratified Random Sampling

Stratified random sampling (SRS) is a fundamental sampling technique that provides accurate estimates for aggregate queries using a small size sample, and has been used widely for approximate query processing. A key question in SRS is how to partition a target sample size among different strata. While Neyman allocation provides a solution that minimizes the variance of an estimate using this sample, it works under the assumption that each stratum is abundant, i.e., has a large number of data points to choose from. This assumption may not hold in general: one or more strata may be bounded, and may not contain a large number of data points, even though the total data size may be large. We first present VOILA, an offline method for allocating sample sizes to strata in a variance-optimal manner, even for the case when one or more strata may be bounded. We next consider SRS on streaming data that are continuously arriving. We show a lower bound, that any streaming algorithm for SRS must have (in the worst case) a variance that is Ω(r) factor away from the optimal, where r is the number of strata. We present S-VOILA, a practical streaming algorithm for SRS that is locally variance-optimal in its allocation of sample sizes to different strata. Our result from experiments on real and synthetic data show that VOILA can have significantly (1.4 to 50.0 times) smaller variance than Neyman allocation. The streaming algorithm S-VOILA results in a variance that is typically close to VOILA, which was given the entire input beforehand.

cs.DB↗