Maximum Likelihood Estimation Over Directed Acyclic Gaussian Graphs.

IF 2.1 4区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Statistical Analysis and Data Mining Pub Date : 2012-12-01 DOI:10.1002/sam.11168

Yiping Yuan, Xiaotong Shen, Wei Pan

引用次数: 0

Abstract

Estimation of multiple directed graphs becomes challenging in the presence of inhomogeneous data, where directed acyclic graphs (DAGs) are used to represent causal relations among random variables. To infer causal relations among variables, we estimate multiple DAGs given a known ordering in Gaussian graphical models. In particular, we propose a constrained maximum likelihood method with nonconvex constraints over elements and element-wise differences of adjacency matrices, for identifying the sparseness structure as well as detecting structural changes over adjacency matrices of the graphs. Computationally, we develop an efficient algorithm based on augmented Lagrange multipliers, the difference convex method, and a novel fast algorithm for solving convex relaxation subproblems. Numerical results suggest that the proposed method performs well against its alternatives for simulated and real data.

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有向无环高斯图上的最大似然估计。

有向无环图（DAG）用于表示随机变量之间的因果关系，在存在不均匀数据的情况下，估计多个有向图变得具有挑战性。为了推断变量之间的因果关系，我们在高斯图模型中给定已知排序的情况下估计多个 DAG。特别是，我们提出了一种约束最大似然法，该方法对邻接矩阵的元素和元素向差具有非凸约束，用于识别稀疏性结构以及检测图邻接矩阵的结构变化。在计算方面，我们开发了一种基于增强拉格朗日乘数、差凸法的高效算法，以及一种用于解决凸松弛子问题的新型快速算法。数值结果表明，在模拟数据和真实数据方面，所提出的方法与其他方法相比表现良好。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistical Analysis and Data Mining COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCEC-COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.20

自引率

7.70%

发文量

期刊介绍： Statistical Analysis and Data Mining addresses the broad area of data analysis, including statistical approaches, machine learning, data mining, and applications. Topics include statistical and computational approaches for analyzing massive and complex datasets, novel statistical and/or machine learning methods and theory, and state-of-the-art applications with high impact. Of special interest are articles that describe innovative analytical techniques, and discuss their application to real problems, in such a way that they are accessible and beneficial to domain experts across science, engineering, and commerce. The focus of the journal is on papers which satisfy one or more of the following criteria: Solve data analysis problems associated with massive, complex datasets Develop innovative statistical approaches, machine learning algorithms, or methods integrating ideas across disciplines, e.g., statistics, computer science, electrical engineering, operation research. Formulate and solve high-impact real-world problems which challenge existing paradigms via new statistical and/or computational models Provide survey to prominent research topics.