# Bayesian Matrix Completion Under Geometric Constraints

arXiv: https://arxiv.org/abs/2601.22765 · HTML: https://mlsanity.com/paper/2601.22765/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 6 of 6)

- [Exact Reconstruction of Euclidean Distance Geometry Problem Using Low-rank Matrix Completion](https://mlsanity.com/paper/1804.04310/) (2018)
- [Fast Low-Rank Bayesian Matrix Completion with Hierarchical Gaussian Prior Models](https://mlsanity.com/paper/1708.02455/) (2017)
- [Solving Partial Differential Equations on Manifolds From Incomplete Inter-Point Distance](https://mlsanity.com/paper/1701.02843/) (2017)
- [Distance Shrinkage and Euclidean Embedding via Regularized Kernel Estimation](https://mlsanity.com/paper/1409.5009/) (2014)
- [Bayesian uncertainty analysis for underwater 3D reconstruction with neural radiance fields](https://mlsanity.com/paper/2407.08154/) (2024)
- [A Bayesian Perspective on Uncertainty Quantification for Estimated Graph Signals](https://mlsanity.com/paper/2502.12971/) (2025)

## Abstract (arXiv)

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.