Mixtures of shifted asymmetric Laplace distributions were introduced as a tool for model-based clustering that allowed for the direct parameterization of skewness in addition to location and scale. Following common practices, an expectation-maximization algorithm was developed to fit these mixtures. However, adaptations to account for the `infinite likelihood problem' led to fits that gave good classification performance at the expense of parameter recovery. In this paper, we propose a more valuable solution to this problem by developing a novel Bayesian parameter estimation scheme for mixtures of shifted asymmetric Laplace distributions. Through simulation studies, we show that the proposed parameter estimation scheme gives better parameter estimates compared to the expectation-maximization based scheme. In addition, we also show that the classification performance is as good, and in some cases better, than the expectation-maximization based scheme. The performance of both schemes are also assessed using well-known real data sets.

翻译：混合偏移非对称拉普拉斯分布已被引入作为基于模型的聚类工具，允许在位置和尺度参数之外直接刻画偏度。按照常规做法，开发了期望最大化算法来拟合这些混合模型。然而，针对"无穷似然问题"的修正方案虽能获得良好的分类性能，却以参数恢复能力为代价。本文提出了一种更有价值的解决方案，通过为混合偏移非对称拉普拉斯分布开发新型贝叶斯参数估计方案来应对该问题。仿真研究表明，与基于期望最大化的方案相比，所提出的参数估计方案能获得更优的参数估计结果。此外，我们还证明其分类性能与基于期望最大化的方案相当，在某些情况下甚至更优。两个方案的表现也通过知名真实数据集进行了评估。