Hashing is a widely used technique for creating uniformly random numbers from arbitrary data. This is required in a large range of core data-driven operations including indexing, partitioning, filters, and sketches. As such, hashing is a core component in numerous systems including relational data systems, key-value stores, compilers, and networks. Due to both the computational and data heavy nature of hashing, it is a core systems bottleneck. For example, a typical database query in the standard TPC-H benchmark may spend 50% of its total cost in hash tables. Similarly, Google spends at least 2% of its total computational cost on C++ hash tables, resulting in a massive yearly cost footprint just from one hashing operation.

We present Stacked Filters, a new probabilistic filter which is fast and robust similar to query-agnostic filters (such as Bloom and Cuckoo filters), and at the same time brings low false positive rates and sizes similar to classifier-based filters (such as Learned Filters). The core idea is that Stacked Filters incorporate workload knowledge about frequently queried non-existing values. Instead of learning, they structurally incorporate that knowledge using hashing and several sequenced filter layers, indexing both data and frequent negatives. Stacked Filters can also gather workload knowledge on-the-fly and adaptively build the filter. We show experimentally that for a given memory budget, Stacked Filters achieve end-to-end query throughput up to 130x better than the best alternative for a workload, either query-agnostic or classifier-based filters, and depending on where data is (SSD or HDD).

To maintain the accuracy of supervised learning models in the presence of evolving data streams, we provide temporally biased sampling schemes that weight recent data most heavily, with inclusion probabilities for a given data item decaying over time according to a specified “decay function.” We then periodically retrain the models on the current sample. This approach speeds up the training process relative to training on all of the data. Moreover, time-biasing lets the models adapt to recent changes in the data while—unlike in a sliding-window approach—still keeping some old data to ensure robustness in the face of temporary fluctuations and periodicities in the data values. In addition, the sampling-based approach allows existing analytic algorithms for static data to be applied to dynamic streaming data essentially without change. We provide and analyze both a simple sampling scheme (Targeted-Size Time-Biased Sampling (T-TBS)) that probabilistically maintains a target sample size and a novel reservoir-based scheme (Reservoir-Based Time-Biased Sampling (R-TBS)) that is the first to provide both control over the decay rate and a guaranteed upper bound on the sample size. If the decay function is exponential, then control over the decay rate is complete, and R-TBS maximizes both expected sample size and sample-size stability. For general decay functions, the actual item inclusion probabilities can be made arbitrarily close to the nominal probabilities, and we provide a scheme that allows a tradeoff between sample footprint and sample-size stability. R-TBS rests on the notion of a “fractional sample” and allows for data arrival rates that are unknown and time varying (unlike T-TBS). The R-TBS and T-TBS schemes are of independent interest, extending the known set of unequal-probability sampling schemes. We discuss distributed implementation strategies; experiments in Spark illuminate the performance and scalability of the algorithms, and show that our approach can increase machine learning robustness in the face of evolving data.

To maintain the accuracy of supervised learning models in the presence of evolving data streams, we provide temporally-biased sampling schemes that weight recent data most heavily, with inclusion probabilities for a given data item decaying exponentially over time. We then periodically retrain the models on the current sample. This approach speeds up the training process relative to training on all of the data. Moreover, time-biasing lets the models adapt to recent changes in the data while -- unlike in a sliding-window approach -- still keeping some old data to ensure robustness in the face of temporary fluctuations and periodicities in the data values. In addition, the sampling-based approach allows existing analytic algorithms for static data to be applied to dynamic streaming data essentially without change. We provide and analyze both a simple sampling scheme (T-TBS) that probabilistically maintains a target size and a novel reservoir-based scheme (R-TBS) that is the first to provide both complete control over the decay rate and a guaranteed upper bound on the size, while maximizing both expected size and sample-size stability. The latter scheme rests on the notion of a fractional sample and, unlike T-TBS, allows for data arrival rates that are unknown and time varying. R-TBS and T-TBS are of independent interest, extending the known set of unequal-probability sampling schemes. We discuss distributed implementation strategies; experiments in Spark illuminate the performance and scalability of the algorithms, and show that our approach can increase machine learning robustness in the face of evolving data.

While numerous indexing and storage schemes have been developed to address the core functionality of predicate evaluation in data systems, they all require specific workload properties (query selectivity, data distribution, data clustering) to provide good performance and fail in other cases. We present a new class of indexing scheme, termed a Column Sketch, which improves the performance of predicate evaluation independently of workload properties. Column Sketches work primarily through the use of lossy compression schemes which are designed so that the index ingests data quickly, evaluates any query performantly, and has small memory footprint. A Column Sketch works by applying this lossy compression on a value-by-value basis, mapping base data to a representation of smaller fixed width codes. Queries are evaluated affirmatively or negatively for the vast majority of values using the compressed data, and only if needed check the base data for the remaining values. Column Sketches work over column, row, and hybrid storage layouts.

Data structures are critical in any data-driven scenario, but they are notoriously hard to design due to a massive design space and the dependence of performance on workload and hardware which evolve continuously. We present a design engine, the Data Calculator, which enables interactive and semi-automated design of data structures. It brings two innovations. First, it offers a set of fine-grained design primitives that capture the first principles of data layout design: how data structure nodes lay data out, and how they are positioned relative to each other. This allows for a structured description of the universe of possible data structure designs that can be synthesized as combinations of those primitives. The second innovation is computation of performance using learned cost models. These models are trained on diverse hardware and data profiles and capture the cost properties of fundamental data access primitives (e.g., random access). With these models, we synthesize the performance cost of complex operations on arbitrary data structure designs without having to: 1) implement the data structure, 2) run the workload, or even 3) access the target hardware. We demonstrate that the Data Calculator can assist data structure designers and researchers by accurately answering rich what-if design questions on the order of a few seconds or minutes, i.e., computing how the performance (response time) of a given data structure design is impacted by variations in the: 1) design, 2) hardware, 3) data, and 4) query workloads. This makes it effortless to test numerous designs and ideas before embarking on lengthy implementation, deployment, and hardware acquisition steps. We also demonstrate that the Data Calculator can synthesize entirely new designs, auto-complete partial designs, and detect suboptimal design choices.