偏正态数据下众数混合专家回归模型的参数估计

The Parameter Estimation of the Mixture of Expert Regression for Mode Models with Skew-normal Data

混合专家模型是对异质总体数据进行回归、分类和聚类的异构性建模的流行框架.研究基于偏正态分布,提出了众数混合专家回归模型,该模型既对混合偏态数据分类后进行众数建模,同时又对混合比例建模,相比单纯的众数回归模型具有更大的适应性,可以概括和描述众多的实际问题.采用了一种有效的模式识别聚类方法来选择子聚类的数量.分别应用MM算法和梯度下降法辅助的EM算法对模型未知参数进行极大似然估计,通过Monte Carlo模拟试验和实例分析比较,说明本文提出方法的有效性和实用性.

The mixture of expert regression models are popular framework for heterogeneous modeling of heterogeneous population data regression, classification and clustering. Based on the skew-normal data, a mixture mode expert regression model is proposed, which can not only model the mode after the mixture skewness data are classified, but model the mixing proportion. Compared with the simple mode regression model, this model has greater adaptability, and can summarize and describe many practical problems. A productive clustering method via mode identification is applied to select the number of components. MM algorithm and EM algorithm assisted by gradient descent method were respectively used to estimate the unknown parameters of the model with maximum likelihood. The effectiveness and practicability of the proposed method are illustrated by Monte Carlo simulation and case analysis.