论文标题
弯曲因子分析与椭圆形高斯分布
Curved factor analysis with the Ellipsoid-Gaussian distribution
论文作者
论文摘要
需要新模型来表征多元数据中的依赖性。通常使用多元高斯分布，但无法表征数据中的非线性关系。大多数非线性扩展往往是高度复杂的。例如，涉及潜在变量中非线性回归模型的估计。在本文中，我们提出了一类相对简单的椭圆形 - 高斯多元分布，该类别是通过使用高斯线性因子模型来得出的，该模型涉及在单位超球上具有von mises-fisher分布的潜在变量。我们表明，椭圆形 - 高斯分布可以灵活地模拟具有较低维度结构的变量之间的曲面关系。采用贝叶斯的方法，我们提出了基于梯度的大地蒙特卡洛和自适应大都市的混合物，用于后采样。我们得出了基本属性，并说明了椭圆形 - 高斯分布在各种模拟和真实数据应用程序上的实用性。还提供随附的R软件包。
There is a need for new models for characterizing dependence in multivariate data. The multivariate Gaussian distribution is routinely used, but cannot characterize nonlinear relationships in the data. Most non-linear extensions tend to be highly complex; for example, involving estimation of a non-linear regression model in latent variables. In this article, we propose a relatively simple class of Ellipsoid-Gaussian multivariate distributions, which are derived by using a Gaussian linear factor model involving latent variables having a von Mises-Fisher distribution on a unit hyper-sphere. We show that the Ellipsoid-Gaussian distribution can flexibly model curved relationships among variables with lower-dimensional structures. Taking a Bayesian approach, we propose a hybrid of gradient-based geodesic Monte Carlo and adaptive Metropolis for posterior sampling. We derive basic properties and illustrate the utility of the Ellipsoid-Gaussian distribution on a variety of simulated and real data applications. An accompanying R package is also available.
