ترغب بنشر مسار تعليمي؟ اضغط هنا

Selecting Reduced Models in the Cross-Entropy Method

109   0   0.0 ( 0 )
 نشر من قبل Patrick Heas
 تاريخ النشر 2018
  مجال البحث الاحصاء الرياضي
والبحث باللغة English
 تأليف Patrick Heas




اسأل ChatGPT حول البحث

This paper deals with the estimation of rare event probabilities using importance sampling (IS), where an optimal proposal distribution is computed with the cross-entropy (CE) method. Although, IS optimized with the CE method leads to an efficient reduction of the estimator variance, this approach remains unaffordable for problems where the repeated evaluation of the score function represents a too intensive computational effort. This is often the case for score functions related to the solution of a partial differential equation (PDE) with random inputs. This work proposes to alleviate computation by the parsimonious use of a hierarchy of score function approximations in the CE optimization process. The score function approximation is obtained by selecting the surrogate of lowest dimensionality, whose accuracy guarantees to pass the current CE optimization stage. The selection relies on certified upper bounds on the error norm. An asymptotic analysis provides some theoretical guarantees on the efficiency and convergence of the proposed algorithm. Numerical results demonstrate the gain brought by the method in the context of pollution alerts and a system modeled by a PDE.



قيم البحث

اقرأ أيضاً

Permutation tests are commonly used for estimating p-values from statistical hypothesis testing when the sampling distribution of the test statistic under the null hypothesis is not available or unreliable for finite sample sizes. One critical challe nge for permutation tests in genomic studies is that an enormous number of permutations is needed for obtaining reliable estimations of small p-values, which requires intensive computational efforts. In this paper, we develop a computationally efficient algorithm for evaluating small p-values from permutation tests based on an adaptive importance sampling approach, which uses the cross-entropy method for finding the optimal proposal density. Simulation studies and analysis of a real microarray dataset demonstrate that our approach achieves considerable gains in computational efficiency comparing with existing methods.
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 imp ortance 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.
143 - Carter T. Butts 2017
Generation of deviates from random graph models with non-trivial edge dependence is an increasingly important problem. Here, we introduce a method which allows perfect sampling from random graph models in exponential family form (exponential family r andom graph models), using a variant of Coupling From The Past. We illustrate the use of the method via an application to the Markov graphs, a family that has been the subject of considerable research. We also show how the method can be applied to a variant of the biased net models, which are not exponentially parameterized.
Bayesian modelling and computational inference by Markov chain Monte Carlo (MCMC) is a principled framework for large-scale uncertainty quantification, though is limited in practice by computational cost when implemented in the simplest form that req uires simulating an accurate computer model at each iteration of the MCMC. The delayed acceptance Metropolis--Hastings MCMC leverages a reduced model for the forward map to lower the compute cost per iteration, though necessarily reduces statistical efficiency that can, without care, lead to no reduction in the computational cost of computing estimates to a desired accuracy. Randomizing the reduced model for the forward map can dramatically improve computational efficiency, by maintaining the low cost per iteration but also avoiding appreciable loss of statistical efficiency. Randomized maps are constructed by a posteriori adaptive tuning of a randomized and locally-corrected deterministic reduced model. Equivalently, the approximated posterior distribution may be viewed as induced by a modified likelihood function for use with the reduced map, with parameters tuned to optimize the quality of the approximation to the correct posterior distribution. Conditions for adaptive MCMC algorithms allow practical approximations and algorithms that have guaranteed ergodicity for the target distribution. Good statistical and computational efficiencies are demonstrated in examples of calibration of large-scale numerical models of geothermal reservoirs and electrical capacitance tomography.
We propose a new scheme for selecting pool states for the embedded Hidden Markov Model (HMM) Markov Chain Monte Carlo (MCMC) method. This new scheme allows the embedded HMM method to be used for efficient sampling in state space models where the stat e can be high-dimensional. Previously, embedded HMM methods were only applied to models with a one-dimensional state space. We demonstrate that using our proposed pool state selection scheme, an embedded HMM sampler can have similar performance to a well-tuned sampler that uses a combination of Particle Gibbs with Backward Sampling (PGBS) and Metropolis updates. The scaling to higher dimensions is made possible by selecting pool states locally near the current value of the state sequence. The proposed pool state selection scheme also allows each iteration of the embedded HMM sampler to take time linear in the number of the pool states, as opposed to quadratic as in the original embedded HMM sampler. We also consider a model with a multimodal posterior, and show how a technique we term mirroring can be used to efficiently move between the modes.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا