Bayesian Matrix Completion Under Geometric Constraints
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918315547426816 |
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| author | Chiluvuri, Rohit Varma Nannuru, Santosh |
| author_facet | Chiluvuri, Rohit Varma Nannuru, Santosh |
| contents | The completion of a Euclidean distance matrix (EDM) from sparse and noisy observations is a fundamental challenge in signal processing, with applications in sensor network localization, acoustic room reconstruction, molecular conformation, and manifold learning. Traditional approaches, such as rank-constrained optimization and semidefinite programming, enforce geometric constraints but often struggle under sparse or noisy conditions. This paper introduces a hierarchical Bayesian framework that places structured priors directly on the latent point set generating the EDM, naturally embedding geometric constraints. By incorporating a hierarchical prior on latent point set, the model enables automatic regularization and robust noise handling. Posterior inference is performed using a Metropolis-Hastings within Gibbs sampler to handle coupled latent point posterior. Experiments on synthetic data demonstrate improved reconstruction accuracy compared to deterministic baselines in sparse regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22765 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bayesian Matrix Completion Under Geometric Constraints Chiluvuri, Rohit Varma Nannuru, Santosh Signal Processing Machine Learning The completion of a Euclidean distance matrix (EDM) from sparse and noisy observations is a fundamental challenge in signal processing, with applications in sensor network localization, acoustic room reconstruction, molecular conformation, and manifold learning. Traditional approaches, such as rank-constrained optimization and semidefinite programming, enforce geometric constraints but often struggle under sparse or noisy conditions. This paper introduces a hierarchical Bayesian framework that places structured priors directly on the latent point set generating the EDM, naturally embedding geometric constraints. By incorporating a hierarchical prior on latent point set, the model enables automatic regularization and robust noise handling. Posterior inference is performed using a Metropolis-Hastings within Gibbs sampler to handle coupled latent point posterior. Experiments on synthetic data demonstrate improved reconstruction accuracy compared to deterministic baselines in sparse regimes. |
| title | Bayesian Matrix Completion Under Geometric Constraints |
| topic | Signal Processing Machine Learning |
| url | https://arxiv.org/abs/2601.22765 |