GLAD: Learning Sparse Graph Recovery
GLAD: Learning Sparse Graph Recovery
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发表时间：
2019-06
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通讯作者：
H. Shrivastava;Xinshi Chen;Binghong Chen;Guanghui Lan;Srinvas Aluru;Le Song
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作者：
H. Shrivastava;Xinshi Chen;Binghong Chen;Guanghui Lan;Srinvas Aluru;Le Song
从数据中恢复稀疏条件独立图是具有广泛应用的机器学习中的一个基本问题。该问题的一个流行表述是 $\ell_1$ 正则化最大似然估计。许多凸优化算法被设计来解决这个公式以恢复图结构。最近，人们对直接基于数据学习算法的兴趣激增，在这种情况下，学习将经验协方差映射到稀疏精度矩阵。然而，在这种情况下，这是一项具有挑战性的任务，因为矩阵的对称正定性（SPD）和稀疏性在学习算法中不容易实现，并且从数据到精度矩阵的直接映射可能包含许多参数。我们提出了一种深度学习架构 GLAD，它使用交替最小化（AM）算法作为我们的模型归纳偏差，并通过监督学习来学习模型参数。我们证明 GLAD 学习了一个非常紧凑且有效的模型，用于从数据中恢复稀疏图。
Recovering sparse conditional independence graphs from data is a fundamental problem in machine learning with wide applications. A popular formulation of the problem is an $\ell_1$ regularized maximum likelihood estimation. Many convex optimization algorithms have been designed to solve this formulation to recover the graph structure. Recently, there is a surge of interest to learn algorithms directly based on data, and in this case, learn to map empirical covariance to the sparse precision matrix. However, it is a challenging task in this case, since the symmetric positive definiteness (SPD) and sparsity of the matrix are not easy to enforce in learned algorithms, and a direct mapping from data to precision matrix may contain many parameters. We propose a deep learning architecture, GLAD, which uses an Alternating Minimization (AM) algorithm as our model inductive bias, and learns the model parameters via supervised learning. We show that GLAD learns a very compact and effective model for recovering sparse graphs from data.