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外文期刊>Statistics and computing
>Dynamics under local conditions in nonconvex optimization. (2019). arXiv preprint arXiv: 1910.02008 Multiscale stick-breaking mixture models
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Dynamics under local conditions in nonconvex optimization. (2019). arXiv preprint arXiv: 1910.02008 Multiscale stick-breaking mixture models
Bayesian nonparametric density estimation is dominated by single-scale methods, typically exploiting mixture model specifications, exception made for Polya trees prior and allied approaches. In this paper we focus on developing a novel family of multiscale stick-breaking mixture models that inherits some of the advantages of both single-scale nonparametric mixtures and Polya trees. 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 Monte Carlo algorithm for posterior computation is introduced. The performance of the method is illustrated analyzing both synthetic and real datasets consistently showing competitive results both in scenarios favoring single-scale and multiscale methods. The results suggest that the method is well suited to estimate densities with varying degree of smoothness and local features.
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机译：贝叶斯非参数密度估计由单尺度方法为主，通常利用混合模型规格，为Polya树之前和盟友方法制作的例外。在本文中，我们专注于开发一种新颖的多尺度粘性混合模型，其继承了单尺度非参数混合物和多亚树木的一些优势。我们的提案基于混合规范，利用根据大类粘性过程的多尺度泛化来增长的无无规随机重量的混合规范;这种多尺度粘性破坏与特定随机过程配对，生成诱导随机有序的内核功能的参数序列。描述了该系列多尺度粘性混合物的性质。专注于高斯规范，推出了一个Markov Chain Monte Carlo算法，用于后部计算。说明该方法的性能分析了合成和实时数据集，始终显示有利于单规模和多尺度方法的情景中的竞争结果。结果表明，该方法非常适合估计具有不同程度的平滑度和局部特征的密度。
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