论文标题
基于模型的多项式计数数据的聚类
Model based clustering of multinomial count data
论文作者
论文摘要
我们考虑了在复制的多项式数据中推断未知数的簇数的问题。在基于模型的聚类观点下，可以通过估计有或没有协变量的多项式分布的有限混合物来治疗此任务。考虑最大似然（ML）和贝叶斯估计。在最大似然方法下，我们提供了预期的 - 最大化（EM）算法，该算法利用了仔细的初始化过程与M-step中Newton--Raphson方法的脊而实现的稳定的实现相结合。在贝叶斯设置下，设计了嵌入在先前平行的回火方案中的随机梯度马尔可夫链蒙特卡洛（MCMC）算法。根据ML方法中的综合完成的似然标准选择集群数，并估算了贝叶斯案例中过度拟合混合物模型中的非空成分数量。我们的方法在模拟数据中说明，并应用于两个真实数据集。可在https://github.com/mqbssppe/multinomiallogitmix上找到R软件包。
We consider the problem of inferring an unknown number of clusters in replicated multinomial data. Under a model based clustering point of view, this task can be treated by estimating finite mixtures of multinomial distributions with or without covariates. Both Maximum Likelihood (ML) as well as Bayesian estimation are taken into account. Under a Maximum Likelihood approach, we provide an Expectation--Maximization (EM) algorithm which exploits a careful initialization procedure combined with a ridge--stabilized implementation of the Newton--Raphson method in the M--step. Under a Bayesian setup, a stochastic gradient Markov chain Monte Carlo (MCMC) algorithm embedded within a prior parallel tempering scheme is devised. The number of clusters is selected according to the Integrated Completed Likelihood criterion in the ML approach and estimating the number of non-empty components in overfitting mixture models in the Bayesian case. Our method is illustrated in simulated data and applied to two real datasets. An R package is available at https://github.com/mqbssppe/multinomialLogitMix.
