论文标题
具有标量和功能协变量模型的无监督贝叶斯分类
Unsupervised Bayesian classification for models with scalar and functional covariates
论文作者
论文摘要
我们通过潜在的多项式变量考虑无监督的分类，该变量将标量响应分类为混合模型的L组件之一。可以将此过程视为一个层次模型，其第一级模型根据参数分布的混合物对标量响应进行建模，第二级通过具有功能和标量协变量的通用线性模型对混合概率进行建模。将功能协变量视为向量的传统方法不仅受到维数的诅咒，因为功能协变量可以在很小的时间间隔内测量，从而导致高度参数化的模型，而且不能考虑数据的性质。我们使用基础扩展来降低维度和贝叶斯方法，以估计参数，同时提供潜在分类向量的预测。通过模拟研究，我们研究了考虑正常混合模型和泊松分布的零膨胀混合物的方法的行为。我们还将经典吉布斯采样方法的性能与变异贝叶斯推断进行了比较。
We consider unsupervised classification by means of a latent multinomial variable which categorizes a scalar response into one of L components of a mixture model. This process can be thought as a hierarchical model with first level modelling a scalar response according to a mixture of parametric distributions, the second level models the mixture probabilities by means of a generalised linear model with functional and scalar covariates. The traditional approach of treating functional covariates as vectors not only suffers from the curse of dimensionality since functional covariates can be measured at very small intervals leading to a highly parametrised model but also does not take into account the nature of the data. We use basis expansion to reduce the dimensionality and a Bayesian approach to estimate the parameters while providing predictions of the latent classification vector. By means of a simulation study we investigate the behaviour of our approach considering normal mixture model and zero inflated mixture of Poisson distributions. We also compare the performance of the classical Gibbs sampling approach with Variational Bayes Inference.
