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首页> 外文期刊>Journal of the royal statistical society >Prediction with high dimensional regression via hierarchically structured Gaussian mixtures and latent variables
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Prediction with high dimensional regression via hierarchically structured Gaussian mixtures and latent variables

机译：通过分层结构的高斯混合和潜在变量进行高维回归预测

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摘要

We propose a hierarchical Gaussian locally linear mapping structured mixture model, named HGLLiM, to predict low dimensional responses based on high dimensional covariates when the associations between the responses and the covariates are non-linear. For tractability, HGLLiM adopts inverse regression to handle the high dimension and locally linear mappings to capture potentially non-linear relations. Data with similar associations are grouped together to form a cluster. A mixture is composed of several clusters following a hierarchical structure. This structure enables shared covariance matrices and latent factors across smaller clusters to limit the number of parameters to estimate. Moreover, HGLLiM adopts a robust estimation procedure for model stability. We use three real data sets to demonstrate different features of HGLLiM. With the face data set, HGLLiM shows ability to model non-linear relationships through mixtures. With the orange juice data set, we show that the prediction performance of HGLLiM is robust to the presence of outliers. Moreover, we demonstrate that HGLLiM is capable of handling large-scale complex data by using the data acquired from a magnetic resonance vascular fingerprinting study. These examples illustrate the wide applicability of HGLLiM to handle different aspects of a complex data structure in prediction.
机译：我们提出了一个分层的高斯局部线性映射结构化混合模型，称为HGLLiM，当响应和协变量之间的关联为非线性时，可基于高维协变量来预测低维响应。为了易于处理，HGLLiM采用逆回归来处理高维和局部线性映射以捕获潜在的非线性关系。具有相似关联的数据被分组在一起以形成一个集群。混合物由遵循等级结构的几个群集组成。这种结构使较小簇之间的共享协方差矩阵和潜在因子可以限制要估计的参数数量。此外，HGLLiM为模型稳定性采用了可靠的估计程序。我们使用三个真实的数据集来演示HGLLiM的不同功能。使用面部数据集，HGLLiM能够通过混合物对非线性关系进行建模。利用橙汁数据集，我们显示HGLLiM的预测性能对于异常值的存在具有鲁棒性。此外，我们证明了HGLLiM能够通过使用从磁共振血管指纹研究获得的数据来处理大规模复杂数据。这些示例说明了HGLLiM在预测中处理复杂数据结构的不同方面的广泛适用性。

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