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首页> 外文学位 >Acyclic Monte Carlo: Efficient multi-level sampling of undirected graphical models through fast marginalization.
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Acyclic Monte Carlo: Efficient multi-level sampling of undirected graphical models through fast marginalization.

机译：非循环蒙特卡洛：通过快速边缘化，对无向图形模型进行高效的多级采样。

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摘要

We present a method for sampling high-dimensional probability spaces, applicable to Markov fields with both discrete and continuous variables, based on an approximate acyclic representation of the probability density. Our method generalizes and places in a common framework some recent work on computing renormalized Hamiltonians and stochastic multigrid sampling.;An acyclic representation of a probability distribution function (PDF) is obtained when one chooses an ordering of the variables and writes the PDF as a product of conditional probabilities, so that the probability of any variable is conditional only on the variables that precede it in the ordering. An acyclic representation makes the sampling efficient, because it uses the sparsity present in the model. We derive an approximate acyclic representation for general graphs by finding marginals through a fast marginalization scheme. The partial derivatives of the logarithm of the marginal probability are computed approximately through stochastic linear projection onto a polynomial basis, followed by reconstruction of the marginal through integration. The projection is based on an optimized inner product, making possible the use of Gaussian quadrature. Probability distributions involving discrete variables are handled by embedding the PDFs in differentiable extensions. Our algorithm can be extended to the evaluation of renormalized Hamiltonians formed using general renormalization schemes.;The approximate acyclic representation of the PDF is then used for sampling. The variables are sampled in a fixed order, producing independent samples together with their sampling weights. We present an optimized sampling strategy that uses a maximum amount of information to choose individual variable values. The samples are further improved using techniques from particle filtering. We also introduce a block Markov chain Monte Carlo scheme based on the sampling weights. Finally, we present applications of our methodology to the Ising model.
机译：我们基于概率密度的近似非循环表示，提出了一种适用于具有离散变量和连续变量的Markov字段的高维概率空间采样方法。我们的方法归纳了一些关于重新规范化的哈密顿量和随机多网格采样的最新工作并将其放在一个公共框架中;当人们选择变量的排序并将PDF写为产品时，可以获得概率分布函数（PDF）的非循环表示条件概率，因此任何变量的概率仅取决于排序中位于其前面的变量。非循环表示使采样有效，因为它使用了模型中存在的稀疏性。通过通过快速边际化方案找到边际，我们得出了一般图的近似非循环表示。边际概率对数的偏导数是通过将随机线性投影近似到多项式来计算的，然后通过积分重建边际。投影基于优化的内积，可以使用高斯求积。涉及离散变量的概率分布是通过将PDF嵌入可微扩展来处理的。我们的算法可以扩展到使用一般的重归一化方案形成的重归一化哈密顿量的评估。;然后，将PDF的近似非循环表示形式用于采样。变量以固定顺序采样，产生独立的采样及其采样权重。我们提出了一种优化的采样策略，该策略使用最大量的信息来选择各个变量值。使用粒子过滤技术进一步改善了样本。我们还基于采样权重介绍了一个马尔可夫链蒙特卡洛方案。最后，我们将我们的方法论应用于伊辛模型。

著录项

  • 作者

    Kominiarczuk, Jakub K.;

  • 作者单位

    University of California, Berkeley.;

  • 授予单位 University of California, Berkeley.;
  • 学科 Applied Mathematics.
  • 学位 Ph.D.
  • 年度 2013
  • 页码 268 p.
  • 总页数 268
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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