Edge selection based on the geometry of dually flat spaces for Gaussian graphical models
Edge selection based on the geometry of dually flat spaces for Gaussian graphical models
复制标题
高斯图模型中基于双平坦空间几何的边缘选择
DOI：
10.1007/s11222-012-9347-3
复制
发表时间：
2013
影响因子：
2.2
通讯作者：
F.
中科院分区：
文献类型：
--
作者：
Hirose;Y. and Komaki;F.
提出了一种在无向高斯图模型中选择边的方法。我们的算法继承了我们以前的工作，它是最小角度回归(LARS)的扩展，它是基于对偶平坦空间的信息几何。协方差矩阵的逆--浓度矩阵的非对角元素在边缘选择中起着重要的作用。我们的迭代方法同时估计这些元素并选择协方差模型。生成浓度矩阵和独立图的估计对的序列，其长度与矩阵的非对角元素的数目相同。在我们的算法中，图的下一个估计是距离浓度矩阵的最新估计最近的图。浓度矩阵的下一次估计不仅仅是最新估计的投影，而且它被收缩到原点。我们描述了该算法，并给出了一些数据集的结果。此外，我们还对模型的辨识和预测作了一些评论。
We propose a method for selecting edges in undirected Gaussian graphical models. Our algorithm takes after our previous work, an extension of Least Angle Regression (LARS), and it is based on the information geometry of dually flat spaces. Non-diagonal elements of the inverse of the covariance matrix, the concentration matrix, play an important role in edge selection. Our iterative method estimates these elements and selects covariance models simultaneously. A sequence of pairs of estimates of the concentration matrix and an independence graph is generated, whose length is the same as the number of non-diagonal elements of the matrix. In our algorithm, the next estimate of the graph is the nearest graph to the latest estimate of the concentration matrix. The next estimate of the concentration matrix is not just the projection of the latest estimate, and it is shrunk to the origin. We describe the algorithm and show results for some datasets. Furthermore, we give some remarks on model identification and prediction.