Distributed Reconstruction of Nonlinear Networks: An ADMM Approach
This addresses the challenge of scaling network reconstruction to very large systems, which is incremental as it builds on existing methods like CCCP and reweighted lasso.
The paper tackles the problem of reconstructing large-scale nonlinear networks from time-series data by developing a distributed algorithm using ADMM, achieving identification of networks with up to 100,000 nodes.
In this paper, we present a distributed algorithm for the reconstruction of large-scale nonlinear networks. In particular, we focus on the identification from time-series data of the nonlinear functional forms and associated parameters of large-scale nonlinear networks. Recently, a nonlinear network reconstruction problem was formulated as a nonconvex optimisation problem based on the combination of a marginal likelihood maximisation procedure with sparsity inducing priors. Using a convex-concave procedure (CCCP), an iterative reweighted lasso algorithm was derived to solve the initial nonconvex optimisation problem. By exploiting the structure of the objective function of this reweighted lasso algorithm, a distributed algorithm can be designed. To this end, we apply the alternating direction method of multipliers (ADMM) to decompose the original problem into several subproblems. To illustrate the effectiveness of the proposed methods, we use our approach to identify a network of interconnected Kuramoto oscillators with different network sizes (500~100,000 nodes).