论文标题
使用树线性级联的概率建模
Probabilistic Modeling Using Tree Linear Cascades
论文作者
论文摘要
我们介绍了树线性级联，这是一类线性结构方程模型，误差变量是不相关的，但不必是高斯或独立的。我们表明，尽管存在这种薄弱的假设，但这类模型的树结构是可识别的。同样，我们引入了一个约束的回归问题，用于拟合树结构的线性结构方程模型并通过分析解决问题。我们将这些结果连接到高斯图形模型的经典Chow-Liu方法。最后，我们通过给出回归的经验风险形式，并在涉及股票价格的基本示例上说明了我们的理论结果的计算吸引力。
We introduce tree linear cascades, a class of linear structural equation models for which the error variables are uncorrelated but need not be Gaussian nor independent. We show that, in spite of this weak assumption, the tree structure of this class of models is identifiable. In a similar vein, we introduce a constrained regression problem for fitting a tree-structured linear structural equation model and solve the problem analytically. We connect these results to the classical Chow-Liu approach for Gaussian graphical models. We conclude by giving an empirical-risk form of the regression and illustrating the computationally attractive implications of our theoretical results on a basic example involving stock prices.
