论文标题
最有可能的最佳亚采样马尔可夫链蒙特卡洛
Most Likely Optimal Subsampled Markov Chain Monte Carlo
论文作者
论文摘要
马尔可夫链蒙特卡洛（MCMC）要求以不同的参数值评估完整的数据可能性，并且通常在大型数据集上计算上不可行。在本文中，我们提议用根据非均匀的亚采样概率进行的子样本近似近对数似然，并得出了最可能的最佳（MLO）亚采样概率，以更好地近似。与现有的均采样概率相同的现有的MCMC算法相比，我们的MLO子采样MCMC具有较高的估计效率，同一亚采样比。我们还使用子采样的对数可能性的渐近分布来得出一个公式，以确定每个MCMC迭代中所需的子样本大小，以给定的精度水平。该公式用于开发MLO子采样MCMC算法的自适应版本。数值实验表明，所提出的方法的表现优于统一的下采样MCMC。
Markov Chain Monte Carlo (MCMC) requires to evaluate the full data likelihood at different parameter values iteratively and is often computationally infeasible for large data sets. In this paper, we propose to approximate the log-likelihood with subsamples taken according to nonuniform subsampling probabilities, and derive the most likely optimal (MLO) subsampling probabilities for better approximation. Compared with existing subsampled MCMC algorithm with equal subsampling probabilities, our MLO subsampled MCMC has a higher estimation efficiency with the same subsampling ratio. We also derive a formula using the asymptotic distribution of the subsampled log-likelihood to determine the required subsample size in each MCMC iteration for a given level of precision. This formula is used to develop an adaptive version of the MLO subsampled MCMC algorithm. Numerical experiments demonstrate that the proposed method outperforms the uniform subsampled MCMC.
