最近邻 Dirichlet 混合模型
Nearest Neighbor Dirichlet Mixtures
AI总结：
针对贝叶斯混合密度估计依赖 MCMC、计算慢且不稳定的问题，提出最近邻 Dirichlet 混合及并行 Monte Carlo 伪后验算法，并证明渐近性质与实证效果。
摘要：
关于密度估计的贝叶斯方法已有丰富文献，这类方法将未知密度刻画为核的混合。它们在提供估计不确定性量化方面具有优势，同时能够适应多种多样的密度。然而，相对于频率派的局部自适应核方法，贝叶斯方法依赖 Markov chain Monte Carlo 算法，实现起来可能缓慢且不稳定。为在保留贝叶斯方法大部分优势的同时避免其计算缺陷，我们提出一类 nearest neighbor-Dirichlet 混合模型。该方法首先基于标准算法将数据分组为若干邻域。在每个邻域内，密度通过贝叶斯参数模型刻画，例如参数未知的 Gaussian 分布。通过为这些局部核的权重赋予 Dirichlet 先验，我们得到权重与核参数的伪后验。本文提出一种简单且天然并行的 Monte Carlo 算法，用于从所得未知密度的伪后验中抽样。我们证明了良好的渐近性质，并在模拟研究中评估这些方法，还将其应用于分类背景下的一个启发性数据集。
英文摘要：
There is a rich literature on Bayesian methods for density estimation, which characterize the unknown density as a mixture of kernels. Such methods have advantages in terms of providing uncertainty quantification in estimation, while being adaptive to a rich variety of densities. However, relative to frequentist locally adaptive kernel methods, Bayesian approaches can be slow and unstable to implement in relying on Markov chain Monte Carlo algorithms. To maintain most of the strengths of Bayesian approaches without the computational disadvantages, we propose a class of nearest neighbor-Dirichlet mixtures. The approach starts by grouping the data into neighborhoods based on standard algorithms. Within each neighborhood, the density is characterized via a Bayesian parametric model, such as a Gaussian with unknown parameters. Assigning a Dirichlet prior to the weights on these local kernels, we obtain a pseudo-posterior for the weights and kernel parameters. A simple and embarrassingly parallel Monte Carlo algorithm is proposed to sample from the resulting pseudo-posterior for the unknown density. Desirable asymptotic properties are shown, and the methods are evaluated in simulation studies and applied to a motivating data set in the context of classification.
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。
