论文标题
dbsop：一种在多面体上快速采样的有效启发式启发式
DBSOP: An Efficient Heuristic for Speedy MCMC Sampling on Polytopes
论文作者
论文摘要
马尔可夫链蒙特卡洛（MCMC）技术长期以来一直在计算几何学对象中进行了研究，这些问题要研究的问题是复杂的几何对象，其性质就需要将优化的技术部署或获得有用的见解。 MCMC方法直接回答了我们试图回答的几何问题，以及如何从理论到实践中部署这些问题。 Polytope是通过线性不等式约束指定的N维空间中有限的卷，需要特定的近似值。因此，如果不使用这种所需重复量定义为误差范围的属性，则不能执行跨密度多型的采样。在这项工作中，我们提出了一种基于多型的三角测量（缝线）的简单精确抽样方法。此外，我们提出了一种有效的算法，该算法是基于密度的多型采样（DBSOP），以迅速进行MCMC采样，其中进行采样所需的时间明显低于与复杂性的低维度中的现有方法$ \ MATHCAL {o \ MATHCAL {O}^{o}^{*}^{*}^{*} \ left（n^n^{n^{3} {3}} $）$。最终，我们强调了可能的未来方面，以及如何通过基于储层采样的方法的整合而进一步改善所提出的方案，从而更快，更有效地解决方案。
Markov Chain Monte Carlo (MCMC) techniques have long been studied in computational geometry subjects whereabouts the problems to be studied are complex geometric objects which by their nature require optimized techniques to be deployed or to gain useful insights by them. MCMC approaches are directly answering to geometric problems we are attempting to answer, and how these problems could be deployed from theory to practice. Polytope which is a limited volume in n-dimensional space specified by a collection of linear inequality constraints require specific approximation. Therefore, sampling across density based polytopes can not be performed without the use of such methods in which the amount of repetition required is defined as a property of error margin. In this work we propose a simple accurate sampling approach based on the triangulation (tessellation) of a polytope. Moreover, we propose an efficient algorithm named Density Based Sampling on Polytopes (DBSOP) for speedy MCMC sampling where the time required to perform sampling is significantly lower compared to existing approaches in low dimensions with complexity $\mathcal{O}^{*}\left(n^{3}\right)$. Ultimately, we highlight possible future aspects and how the proposed scheme can be further improved with the integration of reservoir-sampling based methods resulting in more speedy and efficient solution.
