Networked Information Aggregation for Binary Classification

Abstract

We study networked binary classification on a directed acyclic graph (DAG), where each agent observes only a subset of the feature coordinates. Agents act sequentially along the DAG: each receives logits from its parents, augments its local features with these logits, fits a logistic predictor by minimizing binary cross-entropy (BCE), and forwards its logit to its outgoing neighbors. We ask whether this sequential distributed protocol achieves information aggregation: can a downstream agent attain small excess loss compared to the best logistic predictor with access to all features? This question was studied for linear regression under squared loss by Kearns, Roth, and Ryu (2026). Extending their guarantees to classification is nontrivial because their squared-loss tools do not directly transfer to BCE with a logistic link. We analyze the resulting sequential logit-passing protocol and prove an excess-loss upper bound of $O(M/\sqrt{D})$ on depth-$D$ paths satisfying the $M$ coverage condition, namely that every contiguous block of $M$ agents collectively observes all features. We also prove complementary hard instances with excess loss at least $\Omega(k/D)$, where $k$ is the feature dimension. Together, these results show that network depth is a fundamental bottleneck for information aggregation in networked logistic regression.