Bayesian Matrix Completion Under Geometric Constraints

• URL: http://arxiv.org/abs/2601.22765v1
• Date: Fri, 30 Jan 2026 09:45:34 GMT
• Title: Bayesian Matrix Completion Under Geometric Constraints
• Authors: Rohit Varma Chiluvuri, Santosh Nannuru,
• Abstract summary: The completion of a Euclidean distance matrix from sparse and noisy observations is a fundamental challenge in signal processing.<n>Traditional approaches, such as rank-constrained optimization and semidefinite programming, enforce geometric constraints but often struggle under sparse or noisy conditions.<n>This paper introduces a hierarchical Bayesian framework that places structured priors directly on the latent point set generating the EDM, naturally embedding geometric constraints.
• Score: 3.5522446024799064
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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