Polynomial Graphical Lasso: Learning Edges from Gaussian Graph-Stationary Signals
This is an incremental advancement in graph learning, addressing the problem of modeling nodal relationships more flexibly for applications in graph-aware signal analysis.
The paper tackles the problem of learning graph structures from nodal signals by introducing Polynomial Graphical Lasso (PGL), which models signals as Gaussian and stationary on the graph, resulting in a method that outperforms several alternatives in numerical simulations.
This paper introduces Polynomial Graphical Lasso (PGL), a new approach to learning graph structures from nodal signals. Our key contribution lies in modeling the signals as Gaussian and stationary on the graph, enabling the development of a graph-learning formulation that combines the strengths of graphical lasso with a more encompassing model. Specifically, we assume that the precision matrix can take any polynomial form of the sought graph, allowing for increased flexibility in modeling nodal relationships. Given the resulting complexity and nonconvexity of the resulting optimization problem, we (i) propose a low-complexity algorithm that alternates between estimating the graph and precision matrices, and (ii) characterize its convergence. We evaluate the performance of PGL through comprehensive numerical simulations using both synthetic and real data, demonstrating its superiority over several alternatives. Overall, this approach presents a significant advancement in graph learning and holds promise for various applications in graph-aware signal analysis and beyond.