Estimating Multiple Weighted Networks with Node-Sparse Differences and Shared Low-Rank Structure
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913901114818560 |
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| author | Yan, Hao Levin, Keith |
| author_facet | Yan, Hao Levin, Keith |
| contents | We study the problem of modeling multiple symmetric, weighted networks defined on a common set of nodes, where networks arise from different groups or conditions. We propose a model in which each network is expressed as the sum of a shared low-rank structure and a node-sparse matrix that captures the differences between conditions. This formulation is motivated by practical scenarios, such as in connectomics, where most nodes share a global connectivity structure while only a few exhibit condition-specific deviations. We develop a multi-stage estimation procedure that combines a spectral initialization step, semidefinite programming for support recovery, and a debiased refinement step for low-rank estimation. We establish minimax-optimal guarantees for recovering the shared low-rank component under the row-wise $\ell_{2,\infty}$ norm and elementwise $\ell_{\infty}$ norm, as well as for detecting node-level perturbations under various signal-to-noise regimes. We demonstrate that the availability of multiple networks can significantly enhance estimation accuracy compared to single-network settings. Additionally, we show that commonly-used methods such as group Lasso may provably fail to recover the sparse structure in this setting, a result which might be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15915 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimating Multiple Weighted Networks with Node-Sparse Differences and Shared Low-Rank Structure Yan, Hao Levin, Keith Statistics Theory We study the problem of modeling multiple symmetric, weighted networks defined on a common set of nodes, where networks arise from different groups or conditions. We propose a model in which each network is expressed as the sum of a shared low-rank structure and a node-sparse matrix that captures the differences between conditions. This formulation is motivated by practical scenarios, such as in connectomics, where most nodes share a global connectivity structure while only a few exhibit condition-specific deviations. We develop a multi-stage estimation procedure that combines a spectral initialization step, semidefinite programming for support recovery, and a debiased refinement step for low-rank estimation. We establish minimax-optimal guarantees for recovering the shared low-rank component under the row-wise $\ell_{2,\infty}$ norm and elementwise $\ell_{\infty}$ norm, as well as for detecting node-level perturbations under various signal-to-noise regimes. We demonstrate that the availability of multiple networks can significantly enhance estimation accuracy compared to single-network settings. Additionally, we show that commonly-used methods such as group Lasso may provably fail to recover the sparse structure in this setting, a result which might be of independent interest. |
| title | Estimating Multiple Weighted Networks with Node-Sparse Differences and Shared Low-Rank Structure |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2506.15915 |