Structure Learning via ADMM in Networks obeying Conservation Laws
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| Format: | Preprint |
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2025
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| _version_ | 1866916849523884032 |
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| author | Mada, Rohith Reddy Anguluri, Rajasekhar |
| author_facet | Mada, Rohith Reddy Anguluri, Rajasekhar |
| contents | Learning the edge connectivity structure of networked systems from limited data is a fundamental challenge in many critical infrastructure domains, including power, traffic, and finance. Such systems obey steady-state conservation laws: x = L*y, where x and y represent injected flows (inputs) and potentials (outputs), respectively. The sparsity pattern of the pxp Laplacian L* encodes the underlying edge structure. In a stochastic setting, the goal is to infer this sparsity pattern from zero-mean i.i.d. samples of y.
Recent work by \cite{rayas2022learning} has established statistical consistency results for this learning problem by considering an $\ell_1$-regularized maximum likelihood estimator. However, their approach did not develop a scalable algorithm but relies on solving a convex program via the CVX package. To address this gap, we propose an alternating direction method of multipliers (ADMM), which is transparent and fast. A key contribution is to demonstrate the role of an algebraic matrix Riccati equation in the primal update step of ADMM. Numerical experiments on a host of synthetic and benchmark networks, including power and water systems, show the efficiency of our method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_03189 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure Learning via ADMM in Networks obeying Conservation Laws Mada, Rohith Reddy Anguluri, Rajasekhar Optimization and Control Learning the edge connectivity structure of networked systems from limited data is a fundamental challenge in many critical infrastructure domains, including power, traffic, and finance. Such systems obey steady-state conservation laws: x = L*y, where x and y represent injected flows (inputs) and potentials (outputs), respectively. The sparsity pattern of the pxp Laplacian L* encodes the underlying edge structure. In a stochastic setting, the goal is to infer this sparsity pattern from zero-mean i.i.d. samples of y. Recent work by \cite{rayas2022learning} has established statistical consistency results for this learning problem by considering an $\ell_1$-regularized maximum likelihood estimator. However, their approach did not develop a scalable algorithm but relies on solving a convex program via the CVX package. To address this gap, we propose an alternating direction method of multipliers (ADMM), which is transparent and fast. A key contribution is to demonstrate the role of an algebraic matrix Riccati equation in the primal update step of ADMM. Numerical experiments on a host of synthetic and benchmark networks, including power and water systems, show the efficiency of our method. |
| title | Structure Learning via ADMM in Networks obeying Conservation Laws |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.03189 |