arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2003.04873stat.COcs.DSmath.OCmath.PRstat.ML
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移动目标蒙特卡罗

Moving Target Monte Carlo

Haoyun Ying, Keheng Mao, Klaus Mosegaard

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摘要：

马尔可夫链蒙特卡罗（MCMC）方法在考虑从具有可能未归一化概率密度$p$和观测数据$\mathbf{d}$的高维随机变量$\mathbf{x}$中采样时是流行的。然而，MCMC要求在构造接受率时，在每次迭代中评估建议候选$\mathbf{x}$的后验分布$p(\mathbf{x}|\mathbf{d})$。当这种评价难以处理时，这是昂贵的。本文介绍了一种新的非马尔可夫抽样算法--移动目标蒙特卡罗（MTMC）算法。使用后验分布$a_n(\mathbf{x})$（而不是$p(\mathbf{x}|\mathbf{d})$）的迭代更新近似值构建$n$第次迭代的接受率。仅当候选$\mathbf{x}$被接受时，才计算后验$p(\mathbf{x}|\mathbf{d})$的真值。近似$a_n$利用这些评估并收敛到$p$作为$n \rightarrow \infty$。在不同的情况下，给出了收敛性的证明和收敛速度的估计.

英文摘要：

The Markov Chain Monte Carlo (MCMC) methods are popular when considering sampling from a high-dimensional random variable $\mathbf{x}$ with possibly unnormalised probability density $p$ and observed data $\mathbf{d}$. However, MCMC requires evaluating the posterior distribution $p(\mathbf{x}|\mathbf{d})$ of the proposed candidate $\mathbf{x}$ at each iteration when constructing the acceptance rate. This is costly when such evaluations are intractable. In this paper, we introduce a new non-Markovian sampling algorithm called Moving Target Monte Carlo (MTMC). The acceptance rate at $n$-th iteration is constructed using an iteratively updated approximation of the posterior distribution $a_n(\mathbf{x})$ instead of $p(\mathbf{x}|\mathbf{d})$. The true value of the posterior $p(\mathbf{x}|\mathbf{d})$ is only calculated if the candidate $\mathbf{x}$ is accepted. The approximation $a_n$ utilises these evaluations and converges to $p$ as $n \rightarrow \infty$. A proof of convergence and estimation of convergence rate in different situations are given.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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