Latent Factor Analysis of Gaussian Distributions under Graphical Constraints

Algebraic Properties of Wyner Common Information Solution under Graphical Constraints

The Constrained Minimum Determinant Factor Analysis (CMDFA) setting was motivated by Wyner's common information problem where we seek a latent representation of a given Gaussian vector distribution with the minimum mutual information under certain generative constraints. In this paper, we explore the algebraic structures of the solution space of the CMDFA, when the underlying covariance matrix $Σ_x$ has an additional latent graphical constraint, namely, a latent star topology. In particular, sufficient and necessary conditions in terms of the relationships between edge weights of the star grap…

学习潜在树图模型

Learning Latent Tree Graphical Models

我们研究的问题，学习一个潜在的树图形模型的样本只能从一个子集的变量。我们提出了两个一致的和计算效率高的算法学习最小潜在树，即没有任何冗余的隐藏节点的树。与许多现有方法不同，观察到的节点（或变量）不限于叶节点。我们的第一个算法，递归分组，通过使用所谓的信息距离识别兄弟组递归地构建潜在树。这项工作的主要贡献之一是我们的第二个算法，我们称之为CLINICAL。CLIENT从一个预处理过程开始，在这个过程中，在观察到的变量上构造一棵树。这个全局步骤将在真实潜在树中可能彼此接近的观察到的节点分组，从而指导对小得多的变量子集的后续递归分组（或等效过程）。这导致对潜在树的更准确和更有效的学习。我们还提出了正则化版本的算法，学习潜在的树近似的任意分布。我们提出的算法进行广泛的数值实验，如隐马尔可夫模型和星图的各种潜在的树图形模型，其他方法进行比较。此外，我们证明了我们的方法在现实世界的数据集上的适用性，通过建模的依赖结构的每月股票收益率在标准普尔指数和20个新闻组数据集的话。

Algebraic Properties of Wyner Common Information Solution under Graphical Constraints

The Constrained Minimum Determinant Factor Analysis (CMDFA) setting was motivated by Wyner's common information problem where we seek a latent representation of a given Gaussian vector distribution with the minimum mutual information under certain generative constraints. In this paper, we explore the algebraic structures of the solution space of the CMDFA, when the underlying covariance matrix $Σ_x$ has an additional latent graphical constraint, namely, a latent star topology. In particular, sufficient and necessary conditions in terms of the relationships between edge weights of the star grap…

高斯图模型的有效邻域选择

Efficient Neighborhood Selection for Gaussian Graphical Models

本文讨论了高斯图模型的邻域选择问题。我们提出了两个启发式算法：一个基于互信息检验的一般高斯图模型的前向-后向贪婪算法，和一个基于阈值的算法行走可求和高斯图模型。这两种算法被证明是结构上一致的，和有效的。数值结果表明，这两种算法都能很好地工作。

Latent Factor Analysis of Gaussian Distributions under Graphical Constraints

We explore the algebraic structure of the solution space of convex optimization problem Constrained Minimum Trace Factor Analysis (CMTFA), when the population covariance matrix $Σ_x$ has an additional latent graphical constraint, namely, a latent star topology. In particular, we have shown that CMTFA can have either a rank $ 1 $ or a rank $ n-1 $ solution and nothing in between. The special case of a rank $ 1 $ solution, corresponds to the case where just one latent variable captures all the dependencies among the observables, giving rise to a star topology. We found explicit conditions for bo…

部分高斯图模型估计

Partial Gaussian Graphical Model Estimation

本文研究了高斯图模型在高维经验观测下的部分估计问题。我们推导出一个凸公式，这个问题使用$\ell_1$正则化最大似然估计，这可以通过块坐标下降算法来解决。统计估计性能可以建立我们的方法。所提出的方法具有竞争力的经验性能相比，现有的方法，合成和真实数据集上的各种实验证明。