# Collaboratively Learning Linear Models with Structured Missing Data

arXiv: https://arxiv.org/abs/2307.11947 · HTML: https://mlsanity.com/paper/2307.11947/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 33 references that are in the map.
- First posted on arXiv 22 Jul 2023.

## Builds on (most cited first, 9 of 9)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Private federated learning on vertically partitioned data via entity resolution and additively homomorphic encryption](https://mlsanity.com/paper/1711.10677/) (2017)
- [SecureBoost: A Lossless Federated Learning Framework](https://mlsanity.com/paper/1901.08755/) (2019)
- [Breaking the Communication-Privacy-Accuracy Trilemma](https://mlsanity.com/paper/2007.11707/) (2020)
- [Correlated quantization for distributed mean estimation and optimization](https://mlsanity.com/paper/2203.04925/) (2022)
- [Imputation for High-Dimensional Linear Regression](https://mlsanity.com/paper/2001.09180/) (2020)
- [Optimality guarantees for distributed statistical estimation](https://mlsanity.com/paper/1405.0782/) (2014)

## Built on by (most cited first, 3 of 3)

- [Linear Regression under Missing or Corrupted Coordinates](https://mlsanity.com/paper/2509.19242/) (2025)
- [Concentration Inequalities for Exchangeable Tensors and Matrix-valued Data](https://mlsanity.com/paper/2601.20152/) (2026)
- [Theoretical Analysis of Measure Consistency Regularization for Partially Observed Data](https://mlsanity.com/paper/2602.01437/) (2026)

## Abstract (arXiv)

We study the problem of collaboratively learning least squares estimates for m agents. Each agent observes a different subset of the featuresunicodex2013e.g., containing data collected from sensors of varying resolution. Our goal is to determine how to coordinate the agents in order to produce the best estimator for each agent. We propose a distributed, semi-supervised algorithm Collab, consisting of three steps: local training, aggregation, and distribution. Our procedure does not require communicating the labeled data, making it communication efficient and useful in settings where the labeled data is inaccessible. Despite this handicap, our procedure is nearly asymptotically local minimax optimalunicodex2013even among estimators allowed to communicate the labeled data such as imputation methods. We test our method on real and synthetic data.