非参数反卷积模型
Nonparametric Deconvolution Models
摘要：
我们描述了非参数反卷积模型（NDM），一个家庭的贝叶斯非参数模型的收集数据，其中每个观察是平均的异质粒子的功能。例如，这些类型的数据可以在选举中找到，我们观察每个候选人或投票措施（特征）的个人公民投票（粒子）的选区级投票计数（观察），其中每个选民都是特定选民群体或人口统计（因素）的一部分。与分层狄利克雷过程一样，NDM依赖于两层狄利克雷过程来解释具有未知数量潜在因子的数据;每个观测值都被建模为这些潜在因子的加权平均值。与现有的模型不同，NDM恢复了每个观测的因子分布如何局部变化。这使得NDM不仅可以将每个观测值反卷积为其组成因子，还可以描述每个观测值的特定因子分布如何在观测值之间变化，以及如何偏离相应的全局因子。我们提出了变分推理技术，这一系列的模型，并研究其性能的模拟数据和投票数据从加利福尼亚州。我们表明，包括局部因素，提高了全球因素的估计，并提供了一个新的支架探索数据。
英文摘要：
We describe nonparametric deconvolution models (NDMs), a family of Bayesian nonparametric models for collections of data in which each observation is the average over the features from heterogeneous particles. For example, these types of data are found in elections, where we observe precinct-level vote tallies (observations) of individual citizens' votes (particles) across each of the candidates or ballot measures (features), where each voter is part of a specific voter cohort or demographic (factor). Like the hierarchical Dirichlet process, NDMs rely on two tiers of Dirichlet processes to explain the data with an unknown number of latent factors; each observation is modeled as a weighted average of these latent factors. Unlike existing models, NDMs recover how factor distributions vary locally for each observation. This uniquely allows NDMs both to deconvolve each observation into its constituent factors, and also to describe how the factor distributions specific to each observation vary across observations and deviate from the corresponding global factors. We present variational inference techniques for this family of models and study its performance on simulated data and voting data from California. We show that including local factors improves estimates of global factors and provides a novel scaffold for exploring data.
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