# Networked Information Aggregation via Machine Learning

arXiv: https://arxiv.org/abs/2507.09683 · HTML: https://mlsanity.com/paper/2507.09683/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 13 Jul 2025.

## Builds on (most cited first, 14 of 14)

- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [Loss Minimization through the Lens of Outcome Indistinguishability](https://mlsanity.com/paper/2210.08649/) (2022)
- [Low-Degree Multicalibration](https://mlsanity.com/paper/2203.01255/) (2022)
- [High-Dimensional Prediction for Sequential Decision Making](https://mlsanity.com/paper/2310.17651/) (2023)
- [Multicalibration as Boosting for Regression](https://mlsanity.com/paper/2301.13767/) (2023)
- [Collaborative Prediction: Tractable Information Aggregation via Agreement](https://mlsanity.com/paper/2504.06075/) (2025)
- [Reconciling Individual Probability Forecasts](https://mlsanity.com/paper/2209.01687/) (2022)
- [Tractable Agreement Protocols](https://mlsanity.com/paper/2411.19791/) (2024)
- [How Global Calibration Strengthens Multiaccuracy](https://mlsanity.com/paper/2504.15206/) (2025)
- [Agreement Implies Accuracy for Substitutable Signals](https://mlsanity.com/paper/2111.03278/) (2021)
- [False Consensus, Information Theory, and Prediction Markets](https://mlsanity.com/paper/2206.02993/) (2022)
- [Model Ensembling for Constrained Optimization](https://mlsanity.com/paper/2405.16752/) (2024)
- [Exponentially Fast Parameter Estimation in Networks Using Distributed Dual Averaging](https://mlsanity.com/paper/1309.2350/) (2013)

## Built on by (most cited first, 8 of 8)

- [Networked Information Aggregation for Binary Classification](https://mlsanity.com/paper/2605.01082/) (2026)
- [Optimal Deterministic Multicalibration and Omniprediction](https://mlsanity.com/paper/2606.20557/) (2026)
- [Model Agreement via Anchoring](https://mlsanity.com/paper/2602.23360/) (2026)
- [Optimal Rates for Agentic Networked Information Aggregation](https://mlsanity.com/paper/2609.05318/) (2026)
- [Defensive Boosting for Online Probabilistic Forecasting](https://mlsanity.com/paper/2608.13554/) (2026)
- [Optimal Lower Bounds for Networked Information Aggregation](https://mlsanity.com/paper/2608.15472/) (2026)
- [Optimal Networks for Agentic Information Aggregation](https://mlsanity.com/paper/2609.35537/) (2026)
- [Narrowing the Collaboration Gap, Probably](https://mlsanity.com/paper/2610.19215/) (2026)

## Abstract (arXiv)

We study a distributed learning problem in which learning agents are embedded in a directed acyclic graph (DAG). There is a fixed and arbitrary distribution over feature/label pairs, and each agent or vertex in the graph is able to directly observe only a subset of the features -- potentially a different subset for every agent. The agents learn sequentially in some order consistent with a topological sort of the DAG, committing to a model mapping observations to predictions of the real-valued label. Each agent observes the predictions of their parents in the DAG, and trains their model using both the features of the instance that they directly observe, and the predictions of their parents as additional features. We ask when this process is sufficient to achieve information aggregation, in the sense that some agent in the DAG is able to learn a model whose error is competitive with the best model that could have been learned (in some hypothesis class) with direct access to all features, despite the fact that no single agent in the network has such access. We give upper and lower bounds for this problem for both linear and general hypothesis classes. Our results identify the depth of the DAG as the key parameter: information aggregation can occur over sufficiently long paths in the DAG, assuming that all of the relevant features are well represented along the path, and there are distributions over which information aggregation cannot occur even in the linear case, and even in arbitrarily large DAGs that do not have sufficient depth (such as a hub-and-spokes topology in which the spoke vertices collectively see all the features). We complement our theoretical results with a comprehensive set of experiments.