493,442 research outputs found
The Adaptive Sampling Revisited
The problem of estimating the number of distinct keys of a large
collection of data is well known in computer science. A classical algorithm
is the adaptive sampling (AS). can be estimated by , where is
the final bucket (cache) size and is the final depth at the end of the
process. Several new interesting questions can be asked about AS (some of them
were suggested by P.Flajolet and popularized by J.Lumbroso). The distribution
of is known, we rederive this distribution in a simpler way.
We provide new results on the moments of and . We also analyze the final
cache size distribution. We consider colored keys: assume that among the
distinct keys, do have color . We show how to estimate
. We also study colored keys with some multiplicity given by
some distribution function. We want to estimate mean an variance of this
distribution. Finally, we consider the case where neither colors nor
multiplicities are known. There we want to estimate the related parameters. An
appendix is devoted to the case where the hashing function provides bits with
probability different from
Covariance-Adaptive Slice Sampling
We describe two slice sampling methods for taking multivariate steps using
the crumb framework. These methods use the gradients at rejected proposals to
adapt to the local curvature of the log-density surface, a technique that can
produce much better proposals when parameters are highly correlated. We
evaluate our methods on four distributions and compare their performance to
that of a non-adaptive slice sampling method and a Metropolis method. The
adaptive methods perform favorably on low-dimensional target distributions with
highly-correlated parameters
Adaptive sampling by information maximization
The investigation of input-output systems often requires a sophisticated
choice of test inputs to make best use of limited experimental time. Here we
present an iterative algorithm that continuously adjusts an ensemble of test
inputs online, subject to the data already acquired about the system under
study. The algorithm focuses the input ensemble by maximizing the mutual
information between input and output. We apply the algorithm to simulated
neurophysiological experiments and show that it serves to extract the ensemble
of stimuli that a given neural system ``expects'' as a result of its natural
history.Comment: 4 pages, 2 figure
Ensemble Transport Adaptive Importance Sampling
Markov chain Monte Carlo methods are a powerful and commonly used family of
numerical methods for sampling from complex probability distributions. As
applications of these methods increase in size and complexity, the need for
efficient methods increases. In this paper, we present a particle ensemble
algorithm. At each iteration, an importance sampling proposal distribution is
formed using an ensemble of particles. A stratified sample is taken from this
distribution and weighted under the posterior, a state-of-the-art ensemble
transport resampling method is then used to create an evenly weighted sample
ready for the next iteration. We demonstrate that this ensemble transport
adaptive importance sampling (ETAIS) method outperforms MCMC methods with
equivalent proposal distributions for low dimensional problems, and in fact
shows better than linear improvements in convergence rates with respect to the
number of ensemble members. We also introduce a new resampling strategy,
multinomial transformation (MT), which while not as accurate as the ensemble
transport resampler, is substantially less costly for large ensemble sizes, and
can then be used in conjunction with ETAIS for complex problems. We also focus
on how algorithmic parameters regarding the mixture proposal can be quickly
tuned to optimise performance. In particular, we demonstrate this methodology's
superior sampling for multimodal problems, such as those arising from inference
for mixture models, and for problems with expensive likelihoods requiring the
solution of a differential equation, for which speed-ups of orders of magnitude
are demonstrated. Likelihood evaluations of the ensemble could be computed in a
distributed manner, suggesting that this methodology is a good candidate for
parallel Bayesian computations
Adaptive Threshold Sampling and Estimation
Sampling is a fundamental problem in both computer science and statistics. A
number of issues arise when designing a method based on sampling. These include
statistical considerations such as constructing a good sampling design and
ensuring there are good, tractable estimators for the quantities of interest as
well as computational considerations such as designing fast algorithms for
streaming data and ensuring the sample fits within memory constraints.
Unfortunately, existing sampling methods are only able to address all of these
issues in limited scenarios.
We develop a framework that can be used to address these issues in a broad
range of scenarios. In particular, it addresses the problem of drawing and
using samples under some memory budget constraint. This problem can be
challenging since the memory budget forces samples to be drawn
non-independently and consequently, makes computation of resulting estimators
difficult.
At the core of the framework is the notion of a data adaptive thresholding
scheme where the threshold effectively allows one to treat the non-independent
sample as if it were drawn independently. We provide sufficient conditions for
a thresholding scheme to allow this and provide ways to build and compose such
schemes.
Furthermore, we provide fast algorithms to efficiently sample under these
thresholding schemes
Pushing towards the Limit of Sampling Rate: Adaptive Chasing Sampling
Measurement samples are often taken in various monitoring applications. To
reduce the sensing cost, it is desirable to achieve better sensing quality
while using fewer samples. Compressive Sensing (CS) technique finds its role
when the signal to be sampled meets certain sparsity requirements. In this
paper we investigate the possibility and basic techniques that could further
reduce the number of samples involved in conventional CS theory by exploiting
learning-based non-uniform adaptive sampling.
Based on a typical signal sensing application, we illustrate and evaluate the
performance of two of our algorithms, Individual Chasing and Centroid Chasing,
for signals of different distribution features. Our proposed learning-based
adaptive sampling schemes complement existing efforts in CS fields and do not
depend on any specific signal reconstruction technique. Compared to
conventional sparse sampling methods, the simulation results demonstrate that
our algorithms allow less number of samples for accurate signal
reconstruction and achieve up to smaller signal reconstruction error
under the same noise condition.Comment: 9 pages, IEEE MASS 201
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