# Networked Information Aggregation for Binary Classification

arXiv: https://arxiv.org/abs/2605.01082 · HTML: https://mlsanity.com/paper/2605.01082/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 1 May 2026.

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

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Split learning for health: Distributed deep learning without sharing raw patient data](https://mlsanity.com/paper/1812.00564/) (2018)
- [SecureBoost: A Lossless Federated Learning Framework](https://mlsanity.com/paper/1901.08755/) (2019)
- [Newton Sketch: A Linear-time Optimization Algorithm with Linear-Quadratic Convergence](https://mlsanity.com/paper/1505.02250/) (2015)
- [Iterative Hessian sketch: Fast and accurate solution approximation for constrained least-squares](https://mlsanity.com/paper/1411.0347/) (2014)
- [Oblivious sketching for logistic regression](https://mlsanity.com/paper/2107.06615/) (2021)
- [Vertical Federated Learning: A Structured Literature Review](https://mlsanity.com/paper/2212.00622/) (2022)
- [Networked Information Aggregation via Machine Learning](https://mlsanity.com/paper/2507.09683/) (2025)
- [SecureBoost+: Large Scale and High-Performance Vertical Federated Gradient Boosting Decision Tree](https://mlsanity.com/paper/2110.10927/) (2021)

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

- [Optimal Rates for Agentic Networked Information Aggregation](https://mlsanity.com/paper/2609.05318/) (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)

## Abstract (arXiv)

We study networked binary classification on a directed acyclic graph (DAG) where each agent observes only a subset of the feature columns of a shared dataset. Agents act sequentially along the DAG: each receives prediction columns from its parents (if any), augments its local features with these columns, fits a logistic predictor by minimizing binary cross-entropy (BCE), and forwards its prediction column to its outgoing neighbors. We ask whether this sequential distributed training procedure achieves information aggregation, meaning that some agent attains small excess loss compared to the best logistic predictor trained with access to all feature columns. This question was studied for linear regression under squared loss by Kearns, Roth, and Ryu (SODA 2026). Extending their guarantees to classification is nontrivial because their analysis relies on quadratic structure that does not directly transfer to BCE with a logistic link. We analyze the resulting sequential logit-passing protocol and prove: (i) an excess loss upper bound of O(M/√D) on depth-D paths under the condition that every M contiguous subsequence of M agents collectively observe all features, and (ii) a close lower bound showing instances with excess loss of at least Omega(k/D) where k is the dimension of the feature space. Together, these results identify network depth as a fundamental bottleneck for information aggregation in networked logistic regression.