论文标题
UGLAD：通过优化深度展开的网络来稀疏图恢复
uGLAD: Sparse graph recovery by optimizing deep unrolled networks
论文作者
论文摘要
概率图形模型（PGM）是复杂系统的生成模型。他们依靠变量之间的条件独立性假设来学习稀疏表示，这些表示可以以图形的形式可视化。此类模型用于域中探索和结构发现的域中发现不足的领域。这项工作引入了一种新型技术，可以通过优化深度展开的网络来执行稀疏图恢复。假设输入数据$ x \ in \ mathbb {r}^{m \ times d} $来自基础多元高斯分布，我们对$ x $上的深层模型应用了一个输出Precision Matrix $ \hatθ$的深层模型，这也可以解释为相邻矩阵。我们的模型UGLAD建立在基础上，并将最先进的模型扩展到无监督的环境中。我们模型的关键好处是（1）UGLAD自动优化了与稀疏相关的正则参数，从而比现有算法更好地具有性能。 （2）我们介绍了基于多任务学习的“共识”策略，以在无监督的设置中强大地处理丢失的数据。我们评估模型结果，这些结果是由基因调节网络产生的合成高斯数据，非高斯数据，并在厌氧消化中提出了一个案例研究。
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 $\hatΘ$, 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.
