论文标题
通过信息过滤网络的拓扑正则化
Topological regularization with information filtering networks
论文作者
论文摘要
引入了通过信息过滤网络执行拓扑正则化的方法。该方法可以直接应用于协方差选择问题，从而提供了一种稀疏概率建模的工具，并使用线性和非线性多元概率分布（例如椭圆形和广义双曲线家族）。它也可以直接实现$ l_0 $ norm正规化的多共线回归。在本文中，我详细描述了使用多元学生T进行稀疏建模的应用。针对此稀疏的Student-T案，提出了一种特定的$ L_0 $ NOM-NORM正规化最大化最大化程序。来自股票价格返回和人为生成的数据的真实数据的示例证明了这种方法的适用性，性能和潜力。
A methodology to perform topological regularization via information filtering network is introduced. This methodology can be directly applied to covariance selection problem providing an instrument for sparse probabilistic modeling with both linear and non-linear multivariate probability distributions such as the elliptical and generalized hyperbolic families. It can also be directly implemented for $L_0$-norm regularized multicollinear regression. In this paper, I describe in detail an application to sparse modeling with multivariate Student-t. A specific $L_0$-norm regularized expectation-maximization likelihood maximization procedure is proposed for this sparse Student-t case. Examples with real data from stock prices log-returns and from artificially generated data demonstrate the applicability, performances, and potentials of this methodology.
