Precision Matrix Estimation with Noisy and Missing Data
Precision Matrix Estimation with Noisy and Missing Data
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发表时间：
2019-04
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通讯作者：
Roger Fan;B. Jang;Yuekai Sun;Shuheng Zhou
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作者：
Roger Fan;B. Jang;Yuekai Sun;Shuheng Zhou
估计条件依赖图和精度矩阵是现代统计学和机器学习中最常见的问题。当数据被充分观察时，惩罚最大似然型估计已成为稀疏条件下估计图形模型的标准工具。近年来，这些方法扩展到数据被加性或乘性噪声污染的更复杂的环境中。然而，在这些环境中，不同方法的相对性能并没有得到很好的理解，算法差距仍然存在。特别是，在高维环境中，这些方法需要使用非半正定矩阵作为输入，提出了新的优化挑战。我们开发了一个交替方向的乘法器（ADMM）算法，这些问题，提供了一个可行的算法来估计精度矩阵的不确定输入和潜在的非凸处罚。我们比较这种方法与现有的替代解决方案，并实证表征它们之间的权衡。最后，我们使用这种方法来探索美国参议员之间的网络估计从投票记录数据。
Estimating conditional dependence graphs and precision matrices are some of the most common problems in modern statistics and machine learning. When data are fully observed, penalized maximum likelihood-type estimators have become standard tools for estimating graphical models under sparsity conditions. Extensions of these methods to more complex settings where data are contaminated with additive or multiplicative noise have been developed in recent years. In these settings, however, the relative performance of different methods is not well understood and algorithmic gaps still exist. In particular, in high-dimensional settings these methods require using non-positive semidefinite matrices as inputs, presenting novel optimization challenges. We develop an alternating direction method of multipliers (ADMM) algorithm for these problems, providing a feasible algorithm to estimate precision matrices with indefinite input and potentially nonconvex penalties. We compare this method with existing alternative solutions and empirically characterize the tradeoffs between them. Finally, we use this method to explore the networks among US senators estimated from voting records data.