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Novel Matrix Hit and Run for Sampling Polytopes and Its GPU Implementation
arXiv - CS - Mathematical Software Pub Date : 2021-04-14 , DOI: arxiv-2104.07097 Mario Vazquez Corte, Luis V. Montiel
arXiv - CS - Mathematical Software Pub Date : 2021-04-14 , DOI: arxiv-2104.07097 Mario Vazquez Corte, Luis V. Montiel
We propose and analyze a new Markov Chain Monte Carlo algorithm that
generates a uniform sample over full and non-full dimensional polytopes. This
algorithm, termed "Matrix Hit and Run" (MHAR), is a modification of the Hit and
Run framework. For the regime $n^{1+\frac{1}{3}} \ll m$, MHAR has a lower
asymptotic cost per sample in terms of soft-O notation ($\SO$) than do existing
sampling algorithms after a \textit{warm start}. MHAR is designed to take
advantage of matrix multiplication routines that require less computational and
memory resources. Our tests show this implementation to be substantially faster
than the \textit{hitandrun} R package, especially for higher dimensions.
Finally, we provide a python library based on Pytorch and a Colab notebook with
the implementation ready for deployment in architectures with GPU or just CPU.
中文翻译:
用于采样多边体的新型矩阵即插即用及其GPU实现
我们提出并分析了一种新的马尔可夫链蒙特卡洛算法,该算法可在全维和非全维多形体上生成均匀样本。该算法称为“矩阵命中并运行”(MHAR),是对命中并运行框架的修改。对于$ n ^ {1+ \ frac {1} {3}} \ ll m $而言,MHAR在软O表示法($ \ SO $)方面的每个样本的渐近成本比之后的现有采样算法低\ textit {热启动}。MHAR旨在利用需要较少计算和内存资源的矩阵乘法例程。我们的测试表明,此实现比\ textit {hitandrun} R包要快得多,尤其是对于较大的尺寸。最后,我们提供了一个基于Pytorch的python库和一个Colab笔记本,该实现可随时部署在具有GPU或仅CPU的体系结构中。
更新日期:2021-04-16
中文翻译:
用于采样多边体的新型矩阵即插即用及其GPU实现
我们提出并分析了一种新的马尔可夫链蒙特卡洛算法,该算法可在全维和非全维多形体上生成均匀样本。该算法称为“矩阵命中并运行”(MHAR),是对命中并运行框架的修改。对于$ n ^ {1+ \ frac {1} {3}} \ ll m $而言,MHAR在软O表示法($ \ SO $)方面的每个样本的渐近成本比之后的现有采样算法低\ textit {热启动}。MHAR旨在利用需要较少计算和内存资源的矩阵乘法例程。我们的测试表明,此实现比\ textit {hitandrun} R包要快得多,尤其是对于较大的尺寸。最后,我们提供了一个基于Pytorch的python库和一个Colab笔记本,该实现可随时部署在具有GPU或仅CPU的体系结构中。