论文标题
多尺度破坏混合模型
Multiscale stick-breaking mixture models
论文作者
论文摘要
我们介绍了一个多尺度破坏混合物模型，用于贝叶斯非参数密度估计。贝叶斯非参数文献以单一尺度方法，对Pòlya树和相关方法的例外为主导。我们的建议是基于混合规范，利用了一棵无限深层的二进制重量树，该树是根据大量破坏性过程的多尺度概括而生长的。这种多尺度破坏与特定的随机过程生成了诱导随机有序内核函数的参数序列。描述了这个多尺度破坏混合物家族的特性。为了关注高斯规格，引入了马尔可夫链蒙特卡洛算法用于后验计算。该方法的性能进行了说明，分析了合成和真实数据集。该方法非常适合生活在$ \ mathbb {r} $中的数据，并且能够检测具有不同程度平滑度和本地功能的密度。
We introduce a family of multiscale stick-breaking mixture models for Bayesian nonparametric density estimation. The Bayesian nonparametric literature is dominated by single scale methods, exception made for Pòlya trees and allied approaches. Our proposal is based on a mixture specification exploiting an infinitely-deep binary tree of random weights that grows according to a multiscale generalization of a large class of stick-breaking processes; this multiscale stick-breaking is paired with specific stochastic processes generating sequences of parameters that induce stochastically ordered kernel functions. Properties of this family of multiscale stick-breaking mixtures are described. Focusing on a Gaussian specification, a Markov Chain Montecarlo algorithm for posterior computation is introduced. The performance of the method is illustrated analyzing both synthetic and real data sets. The method is well-suited for data living in $\mathbb{R}$ and is able to detect densities with varying degree of smoothness and local features.
