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这里没有巫术!通过逆协方差估计学习离散图形模型

No voodoo here! Learning discrete graphical models via inverse covariance estimation
课程网址: http://videolectures.net/nips2012_loh_estimation/  
主讲教师: Po-Ling Loh
开课单位: 加利福尼亚大学
开课时间: 2013-01-16
课程语种: 英语
中文简介:
我们研究了广义协方差矩阵的逆的支持与离散图形模型的结构之间的关系。我们证明了对于某些图结构,指标变量的逆协方差矩阵对图的顶点的支持反映了图的条件独立结构。我们的工作扩展了以前仅针对多元高斯分布建立的结果,并且部分地回答了关于非高斯分布的逆协方差矩阵的含义的开放问题。我们提出了基于可能损坏的观测值的具有有界度的一般离散图形模型的图选择方法,并通过模拟验证我们的理论结果。在此过程中,我们还在基于损坏和缺失观测的稀疏高维线性回归设置中建立支持恢复的新结果。
课程简介: We investigate the relationship between the support of the inverses of generalized covariance matrices and the structure of a discrete graphical model. We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional independence structure of the graph. Our work extends results which were previously established only for multivariate Gaussian distributions, and partially answers an open question about the meaning of the inverse covariance matrix of a non-Gaussian distribution. We propose graph selection methods for a general discrete graphical model with bounded degree based on possibly corrupted observations, and verify our theoretical results via simulations. Along the way, we also establish new results for support recovery in the setting of sparse high-dimensional linear regression based on corrupted and missing observations.
关 键 词: 图形模型; 离散图形模型; 多元高斯分布
课程来源: 视频讲座网
最后编审: 2020-07-17:yumf
阅读次数: 56