Probabilistic Graphical Models (PGMs) are generative models of complex systems. They rely on conditional independence assumptions between variables to learn sparse representations which can be visualized in a form of a graph. Such models are used for domain exploration and structure discovery in poorly understood domains. This work introduces a novel technique to perform sparse graph recovery by optimizing deep unrolled networks. Assuming that the input data $X\in\mathbb{R}^{M\times D}$ comes from an underlying multivariate Gaussian distribution, we apply a deep model on $X$ that outputs the precision matrix $\Theta$, which can also be interpreted as the adjacency matrix. Our model, uGLAD, builds upon and extends the state-of-the-art model GLAD to the unsupervised setting. The key benefits of our model are (1) uGLAD automatically optimizes sparsity-related regularization parameters leading to better performance than existing algorithms. (2) We introduce multi-task learning based `consensus' strategy for robust handling of missing data in an unsupervised setting. We evaluate model results on synthetic Gaussian data, non-Gaussian data generated from Gene Regulatory Networks, and present a case study in anaerobic digestion.

翻译：假设输入数据 $X\ in\ mathb{R\\\ m\ times D} 是复杂系统的基因模型, 它们依赖在变量之间有条件的独立假设来学习可以用图表形式呈现的稀少的表达形式。 这些模型用于在不易理解的领域进行域探索和结构发现。 这项工作引入了一种通过优化深层无滚动网络进行稀释图形恢复的新技术。 假设输入数据 $X\ in\ mathb{R\\M\time D$ 来自于一个基本的多变量 Gaussian 分布, 我们应用了一个深层次模型, 用于输出精确矩阵 $\ Theta$, 也可以被解读为相邻矩阵。 我们的模型, uGLAD, 以最先进的模型 GLADAD 为基础, 扩展到未覆盖的设置。 我们模型的主要好处是 (1) uGLADAD自动优化与调制参数相关的调制参数, 导致比现有算法更好的性。 (2) 我们引入一个基于多任务学习的“consenus”战略, 用于在未受监督的磁强处理缺失数据时, 我们评估的合成系统模型分析的模型, 数据库中的数据分析结果。