uGLAD: Sparse graph recovery by optimizing deep unrolled networks
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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∈ℝ^M× D comes from an underlying multivariate Gaussian distribution, we apply a deep model on X that outputs the precision matrix Θ, 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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