For exploratory data analysis, it is often desirable to know what answers you are likely to get before actually obtaining those answers. This can potentially be achieved by designing systems to offer the estimates of a data operation result -- say op(data) -- earlier in the process based on partial data processing. Those estimates continuously refine as more data is processed and finally converge to the exact answer. Unfortunately, the existing techniques -- called Online Aggregation (OLA) -- are limited to a single operation; that is, we cannot obtain the estimates for op(op(data)) or op(...(op(data))). If this Deep OLA becomes possible, data analysts will be able to explore data more interactively using complex cascade operations. In this work, we take a step toward Deep OLA with evolving data frames (edf), a novel data model to offer OLA for nested ops -- op(...(op(data))) -- by representing an evolving structured data (with converging estimates) that is closed under set operations. That is, op(edf) produces yet another edf; thus, we can freely apply successive operations to edf and obtain an OLA output for each op. We evaluate its viability with Wake, an edf-based OLA system, by examining against state-of-the-art OLA and non-OLA systems. In our experiments on TPC-H dataset, Wake produces its first estimates 4.93x faster (median) -- with 1.3x median slowdown for exact answers -- compared to conventional systems. Besides its generality, Wake is also 1.92x faster (median) than existing OLA systems in producing estimates of under 1% relative errors.

翻译：对于探索性数据分析而言，通常希望在实际获得答案之前就能预知可能得到的结果。这可以通过设计系统来实现，即基于部分数据处理过程，更早地提供数据操作结果（例如op(data)）的估计值。这些估计值会随着处理更多数据而持续优化，并最终收敛到精确答案。然而，现有技术（称为在线聚合（OLA））局限于单个操作；也就是说，我们无法获得op(op(data))或op(...(op(data)))的估计值。如果深度在线聚合（Deep OLA）成为可能，数据分析师将能利用复杂的级联操作更具交互性地探索数据。在本工作中，我们通过演进数据框架（evolving data frames, edf）向Deep OLA迈出了一步——这是一种新颖的数据模型，通过表示在集合操作下封闭的演进结构化数据（含收敛估计值），为嵌套操作op(...(op(data)))提供OLA。即，op(edf)产生另一个edf；因此，我们可以自由地将连续操作应用于edf，并为每个操作获得OLA输出。我们通过基于edf的OLA系统Wake，与最先进的OLA及非OLA系统对比评估了其可行性。在TPC-H数据集上的实验中，与常规系统相比，Wake首次估计生成速度中位数提升4.93倍（精确答案中位数仅慢1.3倍）。除通用性外，Wake在生成相对误差低于1%的估计值时，速度中位数比现有OLA系统快1.92倍。