"Wavelet Synopses with Error Guarantees"
Recent work has demonstrated the effectiveness of the wavelet
decomposition in reducing large amounts of data to compact sets
of wavelet coefficients (termed "wavelet synopses") that can
be used to provide fast and reasonably accurate approximate answers to queries.
A major criticism of such techniques is that unlike, for example,
random sampling, conventional wavelet synopses do not provide informative
error guarantees on the accuracy of individual approximate answers.
In fact, as this paper demonstrates, errors can vary widely
(without bound) and unpredictably, even for identical queries on
nearly-identical values in distinct parts of the data.
This lack of error guarantees severely limits the practicality of
traditional wavelets as an approximate query-processing tool, because
users have no idea of the quality of any particular approximate
In this paper, we introduce Probabilistic Wavelet Synopses, the first
wavelet-based data reduction technique with guarantees on the accuracy
of individual approximate answers. Whereas earlier approaches rely on
deterministic thresholding for selecting a set of "good" wavelet
coefficients, our technique is based on a novel, probabilistic
thresholding scheme that assigns each coefficient a probability of
being retained based on its importance to the reconstruction of
individual data values, and then flips coins to select the
synopsis. We show how our scheme avoids the above pitfalls of
deterministic thresholding, providing highly-accurate answers for
individual data values in a data vector. We propose several novel
optimization algorithms for tuning our probabilistic thresholding
scheme to minimize desired error metrics. Experimental results on
real-world and synthetic data sets evaluate these algorithms, and
demonstrate the effectiveness of our probabilistic wavelet synopses in
providing fast, highly-accurate answers with error guarantees.
(in ACM TODS)
my talk slides
Copyright © 2002, Association for Computing Machinery, Inc. (ACM).
Permission to make digital/hard copy of all or part of this material without
fee is granted provided that copies are not made or distributed for profit or
commercial advantage, the ACM copyright/server notice, the title of the
publication and its date appear, and notice is given that copying is by
permission of the Association for Computing Machinery, Inc. (ACM).
To copy otherwise, to republish, to post on servers or to redistribute to lists,
requires prior specific permission and/or a fee.