论文标题
在球形拉普拉斯分布上
On the spherical Laplace distribution
论文作者
论文摘要
长期以来，von mises-fisher（VMF）的分布一直是指导统计中的单位孔虫数据的指导。但是，基于VMF分布的统计推断的性能可能会在数据中存在明显的异常值和噪声时遭受。基于中位数的类比，作为中央趋势及其与拉普拉斯分布的关系的强大度量，我们提出了球形拉普拉斯（SL）分布，这是建模方向数据的新颖概率度量。我们对最大似然估计提出了采样方案和理论结果。在没有封闭式公式的情况下，我们得出有效的数值例程，以进行参数估计。在有限混合模型框架下考虑了基于模型聚类的应用。我们使用模拟和实际数据实验验证了我们用于参数估计和聚类的数值方法。
The von Mises-Fisher (vMF) distribution has long been a mainstay for inference with data on the unit hypersphere in directional statistics. The performance of statistical inference based on the vMF distribution, however, may suffer when there are significant outliers and noise in the data. Based on an analogy of the median as a robust measure of central tendency and its relationship to the Laplace distribution, we proposed the spherical Laplace (SL) distribution, a novel probability measure for modelling directional data. We present a sampling scheme and theoretical results on maximum likelihood estimation. We derive efficient numerical routines for parameter estimation in the absence of closed-form formula. An application of model-based clustering is considered under the finite mixture model framework. Our numerical methods for parameter estimation and clustering are validated using simulated and real data experiments.
