uGLAD: Sparse graph recovery by optimizing deep unrolled networks [article]

Harsh Shrivastava, Urszula Chajewska, Robin Abraham, Xinshi Chen
2022 arXiv   pre-print
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
more » ... tivariate Gaussian distribution, we apply a deep model on X that outputs the precision matrix Θ̂, 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.
arXiv:2205.11610v2 fatcat:wb4ewzoskzeyzpqze236p7wbwi