Corruptions of Supervised Learning Problems: Typology and Mitigations

TL;DR

This paper develops a comprehensive theory of data corruption in supervised learning, unifying models, analyzing impacts on learning, and proposing generalized mitigation strategies for various corruption types.

Contribution

It introduces a unified corruption framework, analyzes effects on learning risks, and extends mitigation methods to handle diverse corruption scenarios.

Findings

Unified corruption model distinguishes different corruption types.

Corruption impacts Bayes risk differently depending on type.

Generalized loss correction methods for attribute and joint corruptions.

Abstract

Corruption is notoriously widespread in data collection. Despite extensive research, the existing literature predominantly focuses on specific settings and learning scenarios, lacking a unified view of corruption modelization and mitigation. In this work, we develop a general theory of corruption, which incorporates all modifications to a supervised learning problem, including changes in model class and loss. Focusing on changes to the underlying probability distributions via Markov kernels, our approach leads to three novel opportunities. First, it enables the construction of a novel, provably exhaustive corruption framework, distinguishing among different corruption types. This serves to unify existing models and establish a consistent nomenclature. Second, it facilitates a systematic analysis of corruption's consequences on learning tasks, by comparing Bayes risks in the clean and corrupted scenarios. Notably, while label corruptions affect only the loss function, attribute corruptions additionally influence the hypothesis class. Third, building upon these results, we investigate mitigations for various corruption types. We expand existing loss-correction methods for label corruption to handle dependent corruption types. Our findings highlight the necessity to generalize this classical corruption-corrected learning framework to a new paradigm with weaker requirements to encompass more corruption types. We provide such a paradigm as well as loss correction formulas in the attribute and joint corruption cases.