Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of sparsity of the underlying model. In this paper, we study the problem of estimating such models exhibiting a more intricate structure comprising simultaneously of sparse, structured sparse and dense components. Such structures naturally arise in several scientific fields, including molecular biology, finance and political science. We introduce a general framework based on a novel structured norm that enables us to estimate such complex structures from high-dimensional data. The resulting optimization problem is convex and we introduce a linearized multi-block alternating direction method of multipliers (ADMM) algorithm to solve it efficiently. We illustrate the superior performance of the proposed framework on a number of synthetic data sets generated from both random and structured networks. Further, we apply the method to a number of real data sets and discuss the results.
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Block-Structured Optimization for Anomalous Pattern Detection in Interdependent Networks
We propose a generalized optimization framework for detecting anomalous patterns (subgraphs that are interesting or unexpected) in interdependent networks, such as multi-layer networks, temporal networks, networks of networks, and many others. We frame the problem as a non-convex optimization that has a general nonlinear score function and a set of block-structured and non-convex constraints. We develop an effective, efficient, and parallelizable projection-based algorithm, namely Graph Block-structured Gradient Projection (GBGP), to solve the problem. It is proved that our algorithm 1) runs in nearly-linear time on the network size, and 2) enjoys a theoretical approximation guarantee. Moreover, we demonstrate how our framework can be applied to two very practical applications, and we conduct comprehensive experiments to show the effectiveness and efficiency of our proposed algorithm.
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- Award ID(s):
- 1954409
- NSF-PAR ID:
- 10187144
- Date Published:
- Journal Name:
- 2019 IEEE International Conference on Data Mining (ICDM)
- Page Range / eLocation ID:
- 1138 to 1143
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICDM.2019.00137
