# Non-Asymptotic Performance of Social Machine Learning Under Limited Data

arXiv: https://arxiv.org/abs/2306.09397 · HTML: https://mlsanity.com/paper/2306.09397/

## Key facts

- Cited by 1 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 15 Jun 2023.

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

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Fast Convergence Rates for Distributed Non-Bayesian Learning](https://mlsanity.com/paper/1508.05161/) (2015)
- [Social Learning and Distributed Hypothesis Testing](https://mlsanity.com/paper/1410.4307/) (2014)
- [Social Learning over Weakly-Connected Graphs](https://mlsanity.com/paper/1609.03703/) (2016)
- [Distributed Detection : Finite-time Analysis and Impact of Network Topology](https://mlsanity.com/paper/1409.8606/) (2014)
- [On the Arithmetic and Geometric Fusion of Beliefs for Distributed Inference](https://mlsanity.com/paper/2204.13741/) (2022)
- [Statistical Hypothesis Testing Based on Machine Learning: Large Deviations Analysis](https://mlsanity.com/paper/2207.10939/) (2022)
- [Interplay between Topology and Social Learning over Weak Graphs](https://mlsanity.com/paper/1910.13905/) (2019)
- [Learning from Heterogeneous Data Based on Social Interactions over Graphs](https://mlsanity.com/paper/2112.09483/) (2021)

## Built on by (most cited first, 1 of 1)

- [Doubly Adaptive Social Learning](https://mlsanity.com/paper/2504.17370/) (2025)

## Abstract (arXiv)

This paper studies the probability of error associated with the social machine learning framework, which involves an independent training phase followed by a cooperative decision-making phase over a graph. This framework addresses the problem of classifying a stream of unlabeled data in a distributed manner. In this work, we examine the classification task with limited observations during the decision-making phase, which requires a non-asymptotic performance analysis. We establish a condition for consistent training and derive an upper bound on the probability of error for classification. The results clarify the dependence on the statistical properties of the data and the combination policy used over the graph. They also establish the exponential decay of the probability of error with respect to the number of unlabeled samples.