4,250 research outputs found
PolyFit: Polynomial-based Indexing Approach for Fast Approximate Range Aggregate Queries
Range aggregate queries find frequent application in data analytics. In some
use cases, approximate results are preferred over accurate results if they can
be computed rapidly and satisfy approximation guarantees. Inspired by a recent
indexing approach, we provide means of representing a discrete point data set
by continuous functions that can then serve as compact index structures. More
specifically, we develop a polynomial-based indexing approach, called PolyFit,
for processing approximate range aggregate queries. PolyFit is capable of
supporting multiple types of range aggregate queries, including COUNT, SUM, MIN
and MAX aggregates, with guaranteed absolute and relative error bounds.
Experiment results show that PolyFit is faster and more accurate and compact
than existing learned index structures.Comment: 13 page
Convex Optimization for Linear Query Processing under Approximate Differential Privacy
Differential privacy enables organizations to collect accurate aggregates
over sensitive data with strong, rigorous guarantees on individuals' privacy.
Previous work has found that under differential privacy, computing multiple
correlated aggregates as a batch, using an appropriate \emph{strategy}, may
yield higher accuracy than computing each of them independently. However,
finding the best strategy that maximizes result accuracy is non-trivial, as it
involves solving a complex constrained optimization program that appears to be
non-linear and non-convex. Hence, in the past much effort has been devoted in
solving this non-convex optimization program. Existing approaches include
various sophisticated heuristics and expensive numerical solutions. None of
them, however, guarantees to find the optimal solution of this optimization
problem.
This paper points out that under (, )-differential privacy,
the optimal solution of the above constrained optimization problem in search of
a suitable strategy can be found, rather surprisingly, by solving a simple and
elegant convex optimization program. Then, we propose an efficient algorithm
based on Newton's method, which we prove to always converge to the optimal
solution with linear global convergence rate and quadratic local convergence
rate. Empirical evaluations demonstrate the accuracy and efficiency of the
proposed solution.Comment: to appear in ACM SIGKDD 201
Oblivious Bounds on the Probability of Boolean Functions
This paper develops upper and lower bounds for the probability of Boolean
functions by treating multiple occurrences of variables as independent and
assigning them new individual probabilities. We call this approach dissociation
and give an exact characterization of optimal oblivious bounds, i.e. when the
new probabilities are chosen independent of the probabilities of all other
variables. Our motivation comes from the weighted model counting problem (or,
equivalently, the problem of computing the probability of a Boolean function),
which is #P-hard in general. By performing several dissociations, one can
transform a Boolean formula whose probability is difficult to compute, into one
whose probability is easy to compute, and which is guaranteed to provide an
upper or lower bound on the probability of the original formula by choosing
appropriate probabilities for the dissociated variables. Our new bounds shed
light on the connection between previous relaxation-based and model-based
approximations and unify them as concrete choices in a larger design space. We
also show how our theory allows a standard relational database management
system (DBMS) to both upper and lower bound hard probabilistic queries in
guaranteed polynomial time.Comment: 34 pages, 14 figures, supersedes: http://arxiv.org/abs/1105.281
Structure-Aware Sampling: Flexible and Accurate Summarization
In processing large quantities of data, a fundamental problem is to obtain a
summary which supports approximate query answering. Random sampling yields
flexible summaries which naturally support subset-sum queries with unbiased
estimators and well-understood confidence bounds.
Classic sample-based summaries, however, are designed for arbitrary subset
queries and are oblivious to the structure in the set of keys. The particular
structure, such as hierarchy, order, or product space (multi-dimensional),
makes range queries much more relevant for most analysis of the data.
Dedicated summarization algorithms for range-sum queries have also been
extensively studied. They can outperform existing sampling schemes in terms of
accuracy on range queries per summary size. Their accuracy, however, rapidly
degrades when, as is often the case, the query spans multiple ranges. They are
also less flexible - being targeted for range sum queries alone - and are often
quite costly to build and use.
In this paper we propose and evaluate variance optimal sampling schemes that
are structure-aware. These summaries improve over the accuracy of existing
structure-oblivious sampling schemes on range queries while retaining the
benefits of sample-based summaries: flexible summaries, with high accuracy on
both range queries and arbitrary subset queries
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
Speculative Approximations for Terascale Analytics
Model calibration is a major challenge faced by the plethora of statistical
analytics packages that are increasingly used in Big Data applications.
Identifying the optimal model parameters is a time-consuming process that has
to be executed from scratch for every dataset/model combination even by
experienced data scientists. We argue that the incapacity to evaluate multiple
parameter configurations simultaneously and the lack of support to quickly
identify sub-optimal configurations are the principal causes. In this paper, we
develop two database-inspired techniques for efficient model calibration.
Speculative parameter testing applies advanced parallel multi-query processing
methods to evaluate several configurations concurrently. The number of
configurations is determined adaptively at runtime, while the configurations
themselves are extracted from a distribution that is continuously learned
following a Bayesian process. Online aggregation is applied to identify
sub-optimal configurations early in the processing by incrementally sampling
the training dataset and estimating the objective function corresponding to
each configuration. We design concurrent online aggregation estimators and
define halting conditions to accurately and timely stop the execution. We apply
the proposed techniques to distributed gradient descent optimization -- batch
and incremental -- for support vector machines and logistic regression models.
We implement the resulting solutions in GLADE PF-OLA -- a state-of-the-art Big
Data analytics system -- and evaluate their performance over terascale-size
synthetic and real datasets. The results confirm that as many as 32
configurations can be evaluated concurrently almost as fast as one, while
sub-optimal configurations are detected accurately in as little as a
fraction of the time
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