Mixture model-based clustering has become an increasingly popular data analysis technique since its introduction over fifty years ago, and is now commonly utilized within a family setting. Families of mixture models arise when the component parameters, usually the component covariance (or scale) matrices, are decomposed and a number of constraints are imposed. Within the family setting, model selection involves choosing the member of the family, i.e., the appropriate covariance structure, in addition to the number of mixture components. To date, the Bayesian information criterion (BIC) has proved most effective for model selection, and the expectation-maximization (EM) algorithm is usually used for parameter estimation. In fact, this EM-BIC rubric has virtually monopolized the literature on families of mixture models. Deviating from this rubric, variational Bayes approximations are developed for parameter estimation and the deviance information criteria (DIC) for model selection. The variational Bayes approach provides an alternate framework for parameter estimation by constructing a tight lower bound on the complex marginal likelihood and maximizing this lower bound by minimizing the associated Kullback-Leibler divergence. The framework introduced, which we refer to as VB-DIC, is applied to the most commonly used family of Gaussian mixture models, and real and simulated data are used to compared with the EM-BIC rubric.

中文翻译：

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用于家庭环境中参数估计和混合模型选择的变分逼近-DIC 量规

自 50 多年前推出以来，基于混合模型的聚类已成为一种日益流行的数据分析技术，现在已在家庭环境中普遍使用。当组件参数（通常是组件协方差（或标度）矩阵）被分解并施加许多约束时，就会出现混合模型族。在家庭环境中，模型选择涉及选择家庭成员，即适当的协方差结构，以及混合成分的数量。迄今为止，贝叶斯信息准则 (BIC) 已被证明对模型选择最有效，而期望最大化 (EM) 算法通常用于参数估计。事实上，这个 EM-BIC 准则实际上垄断了关于混合模型族的文献。偏离这个标题，变分贝叶斯近似被开发用于参数估计和用于模型选择的偏差信息标准 (DIC)。变分贝叶斯方法通过构建复杂边际似然的严格下界并通过最小化相关的 Kullback-Leibler 散度来最大化该下界，为参数估计提供了替代框架。引入的框架，我们称之为 VB-DIC，应用于最常用的高斯混合模型家族，并使用真实和模拟数据与 EM-BIC 标准进行比较。变分贝叶斯方法通过构建复杂边际似然的严格下界并通过最小化相关的 Kullback-Leibler 散度来最大化该下界，为参数估计提供了替代框架。引入的框架，我们称之为 VB-DIC，应用于最常用的高斯混合模型家族，并使用真实和模拟数据与 EM-BIC 标准进行比较。变分贝叶斯方法通过构建复杂边际似然的严格下界并通过最小化相关的 Kullback-Leibler 散度来最大化该下界，为参数估计提供了替代框架。引入的框架，我们称之为 VB-DIC，应用于最常用的高斯混合模型家族，并使用真实和模拟数据与 EM-BIC 标准进行比较。