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Curve prediction and clustering with mixtures of Gaussian process functional regression models

机译：高斯过程函数回归模型混合的曲线预测和聚类

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Shi, Wang, Murray-Smith and Titterington (Biometrics 63:714-723, 2007) proposed a Gaussian process functional regression (GPFR) model to model functional response curves with a set of functional covariates. Two main problems are addressed by their method: modelling nonlinear and nonparametric regression relationship and modelling covariance structure and mean structure simultaneously. The method gives very good results for curve fitting and prediction but side-steps the problem of heterogeneity. In this paper we present a new method for modelling functional data with 'spatially' indexed data, i.e., the heterogeneity is dependent on factors such as region and individual patient's information. For data collected from different sources, we assume that the data corresponding to each curve (or batch) follows a Gaussian process functional regression model as a lower-level model, and introduce an allocation model for the latent indicator variables as a higher-level model. This higher-level model is dependent on the information related to each batch. This method takes advantage of both GPFR and mixture models and therefore improves the accuracy of predictions. The mixture model has also been used for curve clustering, but focusing on the problem of clustering functional relationships between response curve and covariates, i.e. the clustering is based on the surface shape of the functional response against the set of functional covariates. The model is examined on simulated data and real data.
机译：Shi，Wang，Murray-Smith和Titterington（Biometrics 63：714-723，2007）提出了高斯过程功能回归（GPFR）模型，以使用一组功能协变量来建模功能响应曲线。他们的方法解决了两个主要问题：对非线性和非参数回归关系进行建模，同时对协方差结构和均值结构进行建模。该方法为曲线拟合和预测提供了很好的结果，但是避免了异质性问题。在本文中，我们提出了一种使用``空间''索引数据对功能数据进行建模的新方法，即异质性取决于诸如地区和患者个人信息等因素。对于从不同来源收集的数据，我们假定与每个曲线（或批生产）相对应的数据遵循高斯过程函数回归模型作为较低层模型，并为潜在指标变量引入分配模型作为较高层模型。此更高级别的模型取决于与每个批次相关的信息。该方法同时利用了GPFR和混合模型，因此提高了预测的准确性。混合模型也已经用于曲线聚类，但是集中于对响应曲线和协变量之间的功能关系进行聚类的问题，即，聚类基于针对功能协变量的集合的功能响应的表面形状。根据模拟数据和真实数据检查模型。

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