论文标题
在回归中具有强大的可识别性和参数学习，并具有异质响应
Strong identifiability and parameter learning in regression with heterogeneous response
论文作者
论文摘要
回归的混合物是相对于高度不确定且异质响应的感兴趣变量，用于回归学习的强大模型。除了成为给定一些协变量的响应的丰富预测模型外，该模型类别中的参数还提供了有关数据总体中异质性的有用信息，该信息由与许多不同但潜在的亚种相关的响应的条件分布表示。在本文中，我们研究了强大的可识别性，条件密度和参数估计的收敛速率以及在回归模型的有限混合物，确切拟合和过度拟合的设置以及成分数量时，贝叶斯后的收缩行为尚不清楚。该理论适用于链接功能和从业者采用的有条件分布的家庭的共同选择。我们提供了模拟研究和数据图，它阐明了文献中报道的几种流行回归混合模型中发现的参数学习行为。
Mixtures of regression are a powerful class of models for regression learning with respect to a highly uncertain and heterogeneous response variable of interest. In addition to being a rich predictive model for the response given some covariates, the parameters in this model class provide useful information about the heterogeneity in the data population, which is represented by the conditional distributions for the response given the covariates associated with a number of distinct but latent subpopulations. In this paper, we investigate conditions of strong identifiability, rates of convergence for conditional density and parameter estimation, and the Bayesian posterior contraction behavior arising in finite mixture of regression models, under exact-fitted and over-fitted settings and when the number of components is unknown. This theory is applicable to common choices of link functions and families of conditional distributions employed by practitioners. We provide simulation studies and data illustrations, which shed some light on the parameter learning behavior found in several popular regression mixture models reported in the literature.
