# Group-Aware Matrix Estimation and Latent Subspace Recovery

arXiv: https://arxiv.org/abs/2605.20559 · HTML: https://mlsanity.com/paper/2605.20559/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 57 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 10 of 10)

- [Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares](https://mlsanity.com/paper/1410.2596/) (2014)
- [Provable Inductive Matrix Completion](https://mlsanity.com/paper/1306.0626/) (2013)
- [Towards a "universal translator" for neural dynamics at single-cell, single-spike resolution](https://mlsanity.com/paper/2407.14668/) (2024)
- [Comparing high-dimensional neural recordings by aligning their low-dimensional latent representations](https://mlsanity.com/paper/2205.08413/) (2022)
- [Low-Rank Covariance Completion for Graph Quilting with Applications to Functional Connectivity](https://mlsanity.com/paper/2209.08273/) (2022)
- [One Pipeline, Many Transformers: Pattern-Specific Imputation Specialists for Tabular Missing Data](https://mlsanity.com/paper/2510.02625/) (2025)
- [Inpainting the Neural Picture: Inferring Unrecorded Brain Area Dynamics from Multi-Animal Datasets](https://mlsanity.com/paper/2510.11924/) (2025)
- [One-sided Matrix Completion from Two Observations Per Row](https://mlsanity.com/paper/2306.04049/) (2023)
- [Multiple Augmented Reduced Rank Regression for Pan-Cancer Analysis](https://mlsanity.com/paper/2308.16333/) (2023)
- [Penalized matrix decomposition for denoising, compression, and improved demixing of functional imaging data](https://mlsanity.com/paper/1807.06203/) (2018)

## Abstract (arXiv)

Modern matrix completion problems often involve heterogeneous data whose rows simultaneously belong to many meta-categories, such as demographic and age groups in recommendation systems, or region and recording session labels in neural electrophysiological experiments. Standard low-rank estimators impose a single global latent geometry, which can recover average structure but may smooth away subgroup-specific variation, especially when observations are unevenly distributed across groups. We introduce Group-Aware Matrix Estimation (GAME), a convex estimator for overlapping subgroup-wise low-rank matrix estimation. GAME regularizes category-specific submatrices through overlapping nuclear-norm penalties, allowing related groups to borrow information while preserving local latent structure in a shared coordinate system. We provide finite-sample guarantees for both reconstruction error and subgroup-specific subspace recovery, showing how performance depends on sampling density, subgroup rank, and overlap structure. Experiments on synthetic, recommendation, ecological, and neuroscience datasets show that GAME is most beneficial in structured missingness regimes, where subgroup-aware regularization improves both reconstruction accuracy and latent subspace fidelity. Across these benchmarks, GAME is competitive or best among global low-rank, side-information, and modern imputation baselines, with the largest gains when subgroups exhibit distinct low-rank structure.