We consider the problem of estimating multiple related Gaussian graphical models from a high-dimensional data set with observations belonging to distinct classes. We propose the joint graphical lasso, which borrows strength across the classes in order to estimate multiple graphical models that share certain characteristics, such as the locations or weights of nonzero edges. Our approach is based upon maximizing a penalized log likelihood. We employ generalized fused lasso or group lasso penalties, and implement a fast ADMM algorithm to solve the corresponding convex optimization problems. The performance of the proposed method is illustrated through simulated and real data examples.

中文翻译：

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用于跨多个类的逆协方差估计的联合图形套索。

我们考虑从具有属于不同类别的观测值的高维数据集中估计多个相关高斯图形模型的问题。我们提出了联合图形套索，它借用跨类的强度，以估计具有某些特征的多个图形模型，例如非零边的位置或权重。我们的方法基于最大化惩罚对数似然。我们采用广义融合套索或组套索惩罚，并实施快速 ADMM 算法来解决相应的凸优化问题。通过模拟和真实数据示例说明了所提出方法的性能。