Adaptive Shrinkage in Polya Tree Type Models
Adaptive Shrinkage in Polya Tree Type Models
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DOI：
10.1214/16-ba1021
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发表时间：
2017-09-01
影响因子：
4.4
通讯作者：
Ma, Li
中科院分区：
文献类型：
--
作者：
Ma, Li
我们引入了一个层次化的概括波利亚树，采用局部自适应收缩不同尺度的数据特征，同时保持分析的简单性和计算效率。在新模型下的推理使用共轭层次模型的一般配方有效地进行，并且可以非常有效地完成大量观测的数据集。我们在密度估计中说明，所实现的自适应收缩导致适当的平滑，并大大提高了推理。我们评估的性能模型，通过模拟下精心设计的几个示意图的情况下，是代表各种应用。我们比较其性能的波利亚树，可选的波利亚树，和Dirichlet过程的混合物。然后，我们将我们的方法应用于具有455，472个观测值的流式细胞术数据，以实现大量单变量和多变量密度的快速估计，并研究我们的方法在该背景下的计算特性。此外，我们建立的模型，包括绝对连续性，完全非参数，后验一致性的理论保证。所有证据都在补充材料中给出（Ma，2016）。
We introduce a hierarchical generalization to the Polya tree that incorporates locally adaptive shrinkage to data features of different scales, while maintaining analytical simplicity and computational efficiency. Inference under the new model proceeds efficiently using general recipes for conjugate hierarchical models, and can be completed extremely efficiently for data sets with large numbers of observations. We illustrate in density estimation that the achieved adaptive shrinkage results in proper smoothing and substantially improves inference. We evaluate the performance of the model through simulation under several schematic scenarios carefully designed to be representative of a variety of applications. We compare its performance to that of the Polya tree, the optional Polya tree, and the Dirichlet process mixture. We then apply our method to a flow cytometry data with 455,472 observations to achieve fast estimation of a large number of univariate and multivariate densities, and investigate the computational properties of our method in that context. In addition, we establish theoretical guarantees for the model including absolute continuity, full nonparametricity, and posterior consistency. All proofs are given in the Supplementary Material (Ma, 2016).