uGLAD: Sparse graph recovery by optimizing deep unrolled networks

• URL: http://arxiv.org/abs/2205.11610v1
• Date: Mon, 23 May 2022 20:20:27 GMT
• Title: uGLAD: Sparse graph recovery by optimizing deep unrolled networks
• Authors: Harsh Shrivastava, Urszula Chajewska, Robin Abraham, Xinshi Chen
• Abstract summary: We present a novel technique to perform sparse graph recovery by optimizing deep unrolled networks. Our model, uGLAD, builds upon and extends the state-of-the-art model GLAD to the 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.
• Score: 11.48281545083889
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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 $\Theta$, 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.

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