An Adaptive Importance Sampling for Locally Stable Point Processes
The problem of finding the expected value of a statistic of a locally stable point process in a bounded region is addressed. We propose an adaptive importance sampling for solving the problem. In our proposal, we restrict the importance point process to the family of homogeneous Poisson point processes, which enables us to generate quickly independent samples of the importance point process. The optimal intensity of the importance point process is found by applying the cross-entropy minimization method. In the proposed scheme, the expected value of the function and the optimal intensity are iteratively estimated in an adaptive manner. We show that the proposed estimator converges to the target value almost surely, and prove the asymptotic normality of it. We explain how to apply the proposed scheme to the estimation of the intensity of a stationary pairwise interaction point process. The performance of the proposed scheme is compared numerically with the Markov chain Monte Carlo simulation and the perfect sampling.
Code (0)
등록된 구현이 없습니다.
Tasks
Point ProcessesSimilar Papers 제목 키워드 기반
Adaptively Optimised Adaptive Importance Samplers
We introduce a new class of adaptive importance samplers leveraging adaptive optimisation tools, which we term AdaOAIS. We build on Optimised Adaptive Importance Samplers (OAIS), a class of techniques that adapt proposal…
Adaptive Hierarchical Down-Sampling for Point Cloud Classification
While several convolution-like operators have recently been proposed for extracting features out of point clouds, down-sampling an unordered point cloud in a deep neural network has not been rigorously studied. Existing …
ClassificationGeneral ClassificationPoint Cloud ClassificationProposal-Guided Greedy Surrogate Refinement for PDE-Driven High-Dimensional Rare-Event Estimation
Accurate surrogate construction for PDE-driven high-dimensional rare-event simulation is challenging when performance evaluations are expensive. Since a globally accurate surrogate may require many high-fidelity evaluati…
PointLIE: Locally Invertible Embedding for Point Cloud Sampling and Recovery
Point Cloud Sampling and Recovery (PCSR) is critical for massive real-time point cloud collection and processing since raw data usually requires large storage and computation. In this paper, we address a fundamental prob…
The Within-Orbit Adaptive Leapfrog No-U-Turn Sampler
Locally adapting parameters within Markov chain Monte Carlo methods while preserving reversibility is notoriously difficult. The success of the No-U-Turn Sampler (NUTS) largely stems from its clever local adaptation of t…