# Database Alignment with Gaussian Features

arXiv: https://arxiv.org/abs/1903.01422 · HTML: https://mlsanity.com/paper/1903.01422/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2019.

## Built on by (most cited first, 15 of 15)

- [Random Graph Matching in Geometric Models: the Case of Complete Graphs](https://mlsanity.com/paper/2202.10662/) (2022)
- [Correlation detection in trees for planted graph alignment](https://mlsanity.com/paper/2107.07623/) (2021)
- [The Umeyama algorithm for matching correlated Gaussian geometric models in the low-dimensional regime](https://mlsanity.com/paper/2402.15095/) (2024)
- [One-Way Matching of Datasets with Low Rank Signals](https://mlsanity.com/paper/2204.13858/) (2022)
- [On Correlation Detection and Alignment Recovery of Gaussian Databases](https://mlsanity.com/paper/2211.01069/) (2022)
- [Phase Transitions in the Detection of Correlated Databases](https://mlsanity.com/paper/2302.03380/) (2023)
- [Gaussian Database Alignment and Gaussian Planted Matching](https://mlsanity.com/paper/2307.02459/) (2023)
- [Aligning Embeddings and Geometric Random Graphs: Informational Results and Computational Approaches for the Procrustes-Wasserstein Problem](https://mlsanity.com/paper/2405.14532/) (2024)
- [Testing Dependency of Unlabeled Databases](https://mlsanity.com/paper/2311.05874/) (2023)
- [The graph alignment problem: fundamental limits and efficient algorithms](https://mlsanity.com/paper/2404.12418/) (2024)
- [Exact Matching in Correlated Networks with Node Attributes for Improved Community Recovery](https://mlsanity.com/paper/2501.02851/) (2025)
- [Resampling Sensitivity of High-Dimensional PCA](https://mlsanity.com/paper/2212.14531/) (2022)
- [Detection of Correlated Random Vectors](https://mlsanity.com/paper/2401.13429/) (2024)
- [Testing Dependency of Weighted Random Graphs](https://mlsanity.com/paper/2409.14870/) (2024)
- [Sharp Statistical Thresholds for Attributed Gaussian Graph Matching](https://mlsanity.com/paper/2603.23305/) (2026)

## Abstract (arXiv)

We consider the problem of aligning a pair of databases with jointly Gaussian features. We consider two algorithms, complete database alignment via MAP estimation among all possible database alignments, and partial alignment via a thresholding approach of log likelihood ratios. We derive conditions on mutual information between feature pairs, identifying the regimes where the algorithms are guaranteed to perform reliably and those where they cannot be expected to succeed.