1,984 research outputs found
Random Bit Quadrature and Approximation of Distributions on Hilbert Spaces
We study the approximation of expectations \E(f(X)) for Gaussian random
elements with values in a separable Hilbert space and Lipschitz
continuous functionals . We consider restricted Monte Carlo
algorithms, which may only use random bits instead of random numbers. We
determine the asymptotics (in some cases sharp up to multiplicative constants,
in the other cases sharp up to logarithmic factors) of the corresponding -th
minimal error in terms of the decay of the eigenvalues of the covariance
operator of . It turns out that, within the margins from above, restricted
Monte Carlo algorithms are not inferior to arbitrary Monte Carlo algorithms,
and suitable random bit multilevel algorithms are optimal. The analysis of this
problem leads to a variant of the quantization problem, namely, the optimal
approximation of probability measures on by uniform distributions supported
by a given, finite number of points. We determine the asymptotics (up to
multiplicative constants) of the error of the best approximation for the
one-dimensional standard normal distribution, for Gaussian measures as above,
and for scalar autonomous SDEs
Optimizing Lossy Compression Rate-Distortion from Automatic Online Selection between SZ and ZFP
With ever-increasing volumes of scientific data produced by HPC applications,
significantly reducing data size is critical because of limited capacity of
storage space and potential bottlenecks on I/O or networks in writing/reading
or transferring data. SZ and ZFP are the two leading lossy compressors
available to compress scientific data sets. However, their performance is not
consistent across different data sets and across different fields of some data
sets: for some fields SZ provides better compression performance, while other
fields are better compressed with ZFP. This situation raises the need for an
automatic online (during compression) selection between SZ and ZFP, with a
minimal overhead. In this paper, the automatic selection optimizes the
rate-distortion, an important statistical quality metric based on the
signal-to-noise ratio. To optimize for rate-distortion, we investigate the
principles of SZ and ZFP. We then propose an efficient online, low-overhead
selection algorithm that predicts the compression quality accurately for two
compressors in early processing stages and selects the best-fit compressor for
each data field. We implement the selection algorithm into an open-source
library, and we evaluate the effectiveness of our proposed solution against
plain SZ and ZFP in a parallel environment with 1,024 cores. Evaluation results
on three data sets representing about 100 fields show that our selection
algorithm improves the compression ratio up to 70% with the same level of data
distortion because of very accurate selection (around 99%) of the best-fit
compressor, with little overhead (less than 7% in the experiments).Comment: 14 pages, 9 figures, first revisio
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