101 research outputs found
A Novel Nonparametric Density Estimator
We present a novel nonparametric density estimator and a new data-driven bandwidth selection method with excellent properties. The approach is in- spired by the principles of the generalized cross entropy method. The pro- posed density estimation procedure has numerous advantages over the tra- ditional kernel density estimator methods. Firstly, for the first time in the nonparametric literature, the proposed estimator allows for a genuine incor- poration of prior information in the density estimation procedure. Secondly, the approach provides the first data-driven bandwidth selection method that is guaranteed to provide a unique bandwidth for any data. Lastly, simulation examples suggest the proposed approach outperforms the current state of the art in nonparametric density estimation in terms of accuracy and reliability
Three examples of a Practical Exact Markov Chain Sampling
We present three examples of exact sampling from complex multidimensional densities using Markov Chain theory without using coupling from the past techniques. The sampling algorithm presented in the examples also provides a reliable estimate for the normalizing constant of the target densities, which could be useful in Bayesian statistical applications
Semiparametric Cross Entropy for rare-event simulation
The Cross Entropy method is a well-known adaptive importance sampling method
for rare-event probability estimation, which requires estimating an optimal
importance sampling density within a parametric class. In this article we
estimate an optimal importance sampling density within a wider semiparametric
class of distributions. We show that this semiparametric version of the Cross
Entropy method frequently yields efficient estimators. We illustrate the
excellent practical performance of the method with numerical experiments and
show that for the problems we consider it typically outperforms alternative
schemes by orders of magnitude
Kernel density estimation via diffusion
We present a new adaptive kernel density estimator based on linear diffusion
processes. The proposed estimator builds on existing ideas for adaptive
smoothing by incorporating information from a pilot density estimate. In
addition, we propose a new plug-in bandwidth selection method that is free from
the arbitrary normal reference rules used by existing methods. We present
simulation examples in which the proposed approach outperforms existing methods
in terms of accuracy and reliability.Comment: Published in at http://dx.doi.org/10.1214/10-AOS799 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Global Likelihood Optimization Via The Cross-Entropy Method With An Application To Mixture Models
Global likelihood maximization is an important aspect of many statistical analyses. Often the likelihood function is highly multi-extremal. This presents a significant challenge to standard search procedures, which often settle too quickly into an inferior local maximum. We present a new approach based on the cross-entropy (CE) method, and illustrate its use for the analysis of mixture models
Piecewise polynomial approximation of probability density functions with application to uncertainty quantification for stochastic PDEs
The probability density function (PDF) associated with a given set of samples
is approximated by a piecewise-linear polynomial constructed with respect to a
binning of the sample space. The kernel functions are a compactly supported
basis for the space of such polynomials, i.e. finite element hat functions,
that are centered at the bin nodes rather than at the samples, as is the case
for the standard kernel density estimation approach. This feature naturally
provides an approximation that is scalable with respect to the sample size. On
the other hand, unlike other strategies that use a finite element approach, the
proposed approximation does not require the solution of a linear system. In
addition, a simple rule that relates the bin size to the sample size eliminates
the need for bandwidth selection procedures. The proposed density estimator has
unitary integral, does not require a constraint to enforce positivity, and is
consistent. The proposed approach is validated through numerical examples in
which samples are drawn from known PDFs. The approach is also used to determine
approximations of (unknown) PDFs associated with outputs of interest that
depend on the solution of a stochastic partial differential equation
Recognizing Interactions Between People from Video Sequences
his research study proposes a new approach to group activ- ity recognition which is fully automatic. The approach adopted is hierar- chical, starting with tracking and modelling local movement leading to the segmentation of moving regions. Interactions between moving regions are modelled using Kullback-Leibler (KL) divergence. Then the statistics of such movement interactions or as relative positions of moving regions is represented using kernel density estimation (KDE). The dynamics of such movement interactions and relative locations is modelled as well in a development of the approach. Eventually, the KDE representations are subsampled and considered as inputs of a support vector machines (SVM) classifier. The proposed approach does not require any interven- tion by an operato
The cross-entropy method for continuous multi-extremal optimization
In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including those with non-linear constraints
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