A Comprehensive Taxonomy of Corruptions in Supervised Learning Problems and Their Mitigation Strategies

Core Concepts

This work introduces a general information-theoretic framework for modeling and analyzing different types of corruptions in supervised learning problems, going beyond the traditional notion of distribution shift. The proposed taxonomy systematically categorizes corruptions based on their dependence on the input (attributes) and output (labels) spaces, enabling a comprehensive understanding of their impact and mitigation strategies.

Abstract

The paper presents a comprehensive framework for modeling and analyzing corruptions in supervised learning problems. The key points are:

Corruption is defined in a broader sense, encompassing not just changes in data distributions, but also modifications to the model class and loss function. This challenges the traditional view of data as static facts.

An information-theoretic perspective is adopted, using Markov kernels as the foundational mathematical tool. This allows the construction of an exhaustive taxonomy of pairwise Markovian corruptions, categorizing them based on their dependence on the input (attributes) and output (labels) spaces.

The consequences of different corruption types are analyzed by comparing the Bayes risks in the clean and corrupted scenarios. This reveals that corruptions involving attributes can affect both the loss function and the hypothesis class, unlike label-only corruptions which only impact the loss function.

Building on the Bayes risk analysis, the paper investigates mitigation strategies for various corruption types. It identifies the need to generalize the classical corruption-corrected learning framework to include corruptions beyond just labels. The paper provides a negative result, showing that classical loss correction is not sufficient for mitigating attribute and joint corruptions.

A practical example is provided to illustrate the modeling of corruptions using Markov kernels in a finite case.

Overall, the paper presents a unifying framework for understanding and mitigating corruptions in supervised learning, going beyond the traditional focus on distribution shift.

Stats

"Corruption is notoriously widespread in data collection."
"While label corruptions affect only the loss function, more intricate cases involving attribute corruptions extend the influence beyond the loss to affect the hypothesis class."
"We prove that in our setting classical loss correction is still not enough for achieving full mitigation in a corruption setting that involves a attribute corruption, unveiling an additional fundamental difference between label corruption and attribute corruption."

Quotes

"Corruption is notoriously widespread in data collection."
"Corruption includes all modifications of a learning problem, including changes in model class and loss function."
"While label corruptions affect only the loss function, more intricate cases involving attribute corruptions extend the influence beyond the loss to affect the hypothesis class."

Key Insights Distilled From

Corruptions of Supervised Learning Problems: Typology and Mitigations

by Laura Iacovi... at arxiv.org 05-06-2024

https://arxiv.org/pdf/2307.08643.pdf

Deeper Inquiries

How can the proposed framework be extended to handle corruptions involving more than two spaces, such as in multi-domain or concept drift settings

To extend the proposed framework to handle corruptions involving more than two spaces, such as in multi-domain or concept drift settings, we can consider a sequential or parallel composition of multiple corruptions.
In the case of sequential composition, we can apply a series of corruptions one after the other, each transforming the data distribution in a specific way. This sequential corruption model can be represented by chaining multiple Markov kernels, each mapping from one space to another. By combining these kernels in a sequential manner, we can capture the complex transformations that occur across multiple domains or time steps.
On the other hand, in the case of parallel composition, we can consider simultaneous corruptions acting on different spaces independently. This parallel corruption model involves combining multiple Markov kernels in a superposition manner, where each kernel operates on a different space. By superimposing these kernels, we can analyze the joint effects of corruptions across multiple domains or concepts.
By incorporating these sequential and parallel composition strategies into the framework, we can effectively handle corruptions involving more than two spaces. This extension allows for a more comprehensive analysis of complex data dynamics in settings such as multi-domain learning or concept drift scenarios.

What are the implications of non-Markovian corruptions, and how can they be systematically studied within this framework

Non-Markovian corruptions pose unique challenges compared to Markovian corruptions due to their inherent dependencies on previous states or observations. In the context of the proposed framework, studying non-Markovian corruptions requires a more sophisticated analysis of the data dynamics and the impact of historical information on the corruption process.
To systematically study non-Markovian corruptions within this framework, we can consider extending the definition of corruption to include memory or context-dependent transformations. This extension would involve incorporating memory kernels that capture the historical dependencies in the corruption process. By introducing memory kernels and allowing for non-Markovian transformations, we can model more complex and realistic corruption scenarios.
The implications of non-Markovian corruptions are significant, as they can introduce long-term dependencies and intricate patterns in the data distribution. Understanding and mitigating non-Markovian corruptions require a deeper exploration of the temporal relationships and memory effects in the corruption process. By incorporating memory kernels and memory-dependent transformations, we can gain insights into the impact of historical information on the learning task and develop more robust mitigation strategies for non-Markovian corruptions.

Can the information-theoretic perspective provide insights into the fundamental limits of corruption mitigation, beyond the specific algorithms considered

The information-theoretic perspective offers valuable insights into the fundamental limits of corruption mitigation beyond specific algorithms by quantifying the impact of corruption on the learning process. By analyzing the information content and entropy of the corrupted data distribution, we can assess the extent of information loss and the complexity of the corruption effects on the learning task.
The information-theoretic framework allows us to evaluate the efficiency of corruption mitigation strategies by comparing the information content before and after applying the mitigation techniques. This analysis provides a theoretical foundation for understanding the trade-offs between corruption correction and information preservation in the learning process.
Furthermore, the information-theoretic perspective can help identify the fundamental limits of corruption mitigation by quantifying the amount of information that can be recovered or preserved in the presence of different types of corruptions. By studying the information flow and processing inequalities in corrupted data, we can determine the optimal strategies for mitigating corruption while minimizing information loss.
In conclusion, the information-theoretic perspective offers a principled approach to understanding the limits of corruption mitigation in machine learning problems, providing insights into the fundamental constraints and trade-offs involved in combating corruptions beyond specific algorithmic interventions.