论文标题
通过随机预测估算高维伽玛卷积
Estimation of high dimensional Gamma convolutions through random projections
论文作者
论文摘要
多变量广义伽马卷积是由卷积半参数结构定义的分布。它们的灵活依赖结构，边际可能性及其有用的卷积表达使它们吸引了从业者。但是，在尺寸高时安装这样的分布是一个挑战。我们根据（移位）累积物近似的laguerre集成正方形误差的近似提出了随机估计程序，并根据数据集的随机投影进行了评估。通过分析我们通过草个库中的工具分析我们的损失，对度量的稀疏优化和瓦斯坦梯度流，我们显示了随机梯度下降到适当估计较高尺寸分布的适当估计器的收敛性。我们在低维度和高维设置上提出了几个示例。
Multivariate generalized Gamma convolutions are distributions defined by a convolutional semi-parametric structure. Their flexible dependence structures, the marginal possibilities and their useful convolutional expression make them appealing to the practitioner. However, fitting such distributions when the dimension gets high is a challenge. We propose stochastic estimation procedures based on the approximation of a Laguerre integrated square error via (shifted) cumulants approximation, evaluated on random projections of the dataset. Through the analysis of our loss via tools from Grassmannian cubatures, sparse optimization on measures and Wasserstein gradient flows, we show the convergence of the stochastic gradient descent to a proper estimator of the high dimensional distribution. We propose several examples on both low and high-dimensional settings.
