Estimating the selectivity of a query is a key step in almost any cost-based query optimizer. Most of today's databases rely on histograms or samples that are periodically refreshed by re-scanning the data as the underlying data changes. Since frequent scans are costly, these statistics are often stale and lead to poor selectivity estimates. As an alternative to scans, query-driven histograms have been proposed, which refine the histograms based on the actual selectivities of the observed queries. Unfortunately, these approaches are either too costly to use in practice-i.e., require an exponential number of buckets-or quickly lose their advantage as they observe more queries. For example, the state-of-the-art technique requires 318,936 buckets (and over 8 seconds of refinement overhead per query) after observing only 300 queries.In this paper, we propose a selectivity learning framework, called QuickSel, which falls into the query-driven paradigm but does not use histograms. Instead, it builds an internal model of the underlying data, which can be refined significantly faster (e.g., only 1.9 milliseconds for 300 queries). This fast refinement allows QuickSel to continuously learn from each query and yield increasingly more accurate selectivity estimates over time. Unlike query-driven histograms, Quick-Sel relies on a mixture model and a new optimization algorithm for training its model. Our extensive experiments on two real-world datasets confirm that, given the same target accuracy, QuickSel is on average 254.6× faster than stateof-the-art query-driven histograms, including ISOMER and STHoles. Further, given the same space budget, QuickSel is on average 57.3% and 91.1% more accurate than periodicallyupdated histograms and samples, respectively.

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