Database Learning: Toward a Database that Becomes Smarter Every Time

In today's databases, previous query answers rarely benefit answering future queries. For the first time, to the best of our knowledge, we change this paradigm in an approximate query processing (AQP) context. We make the following observation: the answer to each query reveals some degree of knowledge about the answer to another query because their answers stem from the same underlying distribution that has produced the entire dataset. Exploiting and refining this knowledge should allow us to answer queries more analytically, rather than by reading enormous amounts of raw data. Also, processing more queries should continuously enhance our knowledge of the underlying distribution, and hence lead to increasingly faster response times for future queries. We call this novel idea---learning from past query answers---Database Learning. We exploit the principle of maximum entropy to produce answers, which are in expectation guaranteed to be more accurate than existing sample-based approximations. Empowered by this idea, we build a query engine on top of Spark SQL, called Verdict. We conduct extensive experiments on real-world query traces from a large customer of a major database vendor. Our results demonstrate that Verdict supports 73.7% of these queries, speeding them up by up to 23.0x for the same accuracy level compared to existing AQP systems.Comment: This manuscript is an extended report of the work published in ACM SIGMOD conference 201

K-nearest Neighbor Search by Random Projection Forests

K-nearest neighbor (kNN) search has wide applications in many areas, including data mining, machine learning, statistics and many applied domains. Inspired by the success of ensemble methods and the flexibility of tree-based methodology, we propose random projection forests (rpForests), for kNN search. rpForests finds kNNs by aggregating results from an ensemble of random projection trees with each constructed recursively through a series of carefully chosen random projections. rpForests achieves a remarkable accuracy in terms of fast decay in the missing rate of kNNs and that of discrepancy in the kNN distances. rpForests has a very low computational complexity. The ensemble nature of rpForests makes it easily run in parallel on multicore or clustered computers; the running time is expected to be nearly inversely proportional to the number of cores or machines. We give theoretical insights by showing the exponential decay of the probability that neighboring points would be separated by ensemble random projection trees when the ensemble size increases. Our theory can be used to refine the choice of random projections in the growth of trees, and experiments show that the effect is remarkable.Comment: 15 pages, 4 figures, 2018 IEEE Big Data Conferenc

Learning multi-view neighborhood preserving projections

We address the problem of metric learning for multi-view data, namely the construction of embedding projections from data in different representations into a shared feature space, such that the Euclidean distance in this space provides a meaningful within-view as well as between-view similarity. Our motivation stems from the problem of cross-media retrieval tasks, where the availability of a joint Euclidean distance function is a prerequisite to allow fast, in particular hashing-based, nearest neighbor queries. We formulate an objective function that expresses the intuitive concept that matching samples are mapped closely together in the output space, whereas non-matching samples are pushed apart, no matter in which view they are available. The resulting optimization problem is not convex, but it can be decomposed explicitly into a convex and a concave part, thereby allowing efficient optimization using the convex-concave procedure. Experiments on an image retrieval task show that nearest-neighbor based cross-view retrieval is indeed possible, and the proposed technique improves the retrieval accuracy over baseline techniques

Speeding up neighborhood search in local Gaussian process prediction

Recent implementations of local approximate Gaussian process models have pushed computational boundaries for non-linear, non-parametric prediction problems, particularly when deployed as emulators for computer experiments. Their flavor of spatially independent computation accommodates massive parallelization, meaning that they can handle designs two or more orders of magnitude larger than previously. However, accomplishing that feat can still require massive supercomputing resources. Here we aim to ease that burden. We study how predictive variance is reduced as local designs are built up for prediction. We then observe how the exhaustive and discrete nature of an important search subroutine involved in building such local designs may be overly conservative. Rather, we suggest that searching the space radially, i.e., continuously along rays emanating from the predictive location of interest, is a far thriftier alternative. Our empirical work demonstrates that ray-based search yields predictors with accuracy comparable to exhaustive search, but in a fraction of the time - bringing a supercomputer implementation back onto the desktop.Comment: 24 pages, 5 figures, 4 table