# A method of supervised learning from conflicting data with hidden contexts

arXiv: https://arxiv.org/abs/2108.12113 · HTML: https://mlsanity.com/paper/2108.12113/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 27 Aug 2021.

## Abstract (arXiv)

Conventional supervised learning assumes a stable input-output relationship. However, this assumption fails in open-ended training settings where the input-output relationship depends on hidden contexts. In this work, we formulate a more general supervised learning problem in which training data is drawn from multiple unobservable domains, each potentially exhibiting distinct input-output maps. This inherent conflict in data renders standard empirical risk minimization training ineffective. To address this challenge, we propose a method LEAF that introduces an allocation function, which learns to assign conflicting data to different predictive models. We establish a connection between LEAF and a variant of the Expectation-Maximization algorithm, allowing us to derive an analytical expression for the allocation function. Finally, we provide a theoretical analysis of LEAF and empirically validate its effectiveness on both synthetic and real-world tasks involving conflicting data.