Q-error -- the standard metric for quantifying the error of individual cardinality estimates -- has been widely adopted as a surrogate for query plan optimality in recent work on learning-based cardinality estimation. However, the only result connecting Q-error with plan optimality is an upper-bound on the cost of the worst possible query plan computed from a set of cardinality estimates---there is no connection between Q-error and the real plans generated by standard query optimizers. Therefore, in order to identify sub-optimal query plans, we propose a learning-based method having as its main feature a novel measure called L1-error. Similar to Q-error, L1-error requires complete knowledge of true cardinalities and estimates for all the sub-plans of a query plan. Unlike Q-error, which considers the estimates independently, L1-error is defined as a permutation distance between true cardinalities and estimates for all the sub-plans having the same number of joins. Moreover, L1-error takes into account errors relative to the magnitude of their cardinalities and gives larger weight to small multi-way joins. Our experimental results confirm that, when L1-error is integrated into a standard decision tree classifier, it leads to the accurate identification of sub-optimal plans across four different benchmarks. This accuracy can be further improved by combining L1-error with Q-error into a composite feature that can be computed without overhead from the same data.

Sketches are single-pass small-space data summaries that can quickly estimate the cardinality of join queries. However, sketches are not directly applicable to join queries with dynamic filter conditions --- where arbitrary selection predicate(s) are applied --- since a sketch is limited to a fixed selection. While multiple sketches for various selections can be used in combination, they each incur individual storage and maintenance costs. Alternatively, exact sketches can be built during runtime for every selection. To make this process scale, a high-degree of parallelism --- available in hardware accelerators such as GPUs --- is required. Therefore, sketch usage for cardinality estimation in query optimization is limited. Following recent work that applies transformers to cardinality estimation, we design a novel learning-based method to approximate the sketch of any arbitrary selection, enabling sketches for join queries with filter conditions. We train a transformer on each table to estimate the sketch of any subset of the table, i.e., any arbitrary selection. Transformers achieve this by learning the joint distribution amongst table attributes, which is equivalent to a multidimensional sketch. Subsequently, transformers can approximate any sketch, enabling sketches for join cardinality estimation. In turn, estimating joins via approximate sketches allows tables to be modeled individually and thus scales linearly with the number of tables. We evaluate the accuracy and efficacy of approximate sketches on queries with selection predicates consisting of conjunctions of point and range conditions. Approximate sketches achieve similar accuracy to exact sketches with at least one order of magnitude less overhead.

Consider a set of black-box models – each of them independently trained on a different dataset – answering the same predictive spatio-temporal query. Being built in isolation, each model traverses its own life-cycle until it is deployed to production, learning data patterns from different datasets and facing independent hyper-parameter tuning. In order to answer the query, the set of black-box predictors has to be ensembled and allocated to the spatio-temporal query region. However, computing an optimal ensemble is a complex task that involves selecting the appropriate models and defining an effective allocation strategy that maps the models to the query region. In this paper we present DJEnsemble, a cost-based strategy for the automatic selection and allocation of a disjoint ensemble of black-box predictors to answer predictive spatio-temporal queries. We conduct a set of extensive experiments that evaluate DJEnsemble and highlight its efficiency, selecting model ensembles that are almost as efficient as the optimal solution. When compared against the traditional ensemble approach, DJEnsemble achieves up to 4X improvement in execution time and almost 9X improvement in prediction accuracy.