Multi-Class Classification with Abstention: Theoretical Analysis and Algorithms

Core Concepts

The authors present new theoretical and algorithmic results for multi-class classification with abstention in the predictor-rejector framework, including introducing new surrogate losses with strong consistency guarantees.

Abstract

The authors study the problem of multi-class classification with abstention, where the learner can choose to abstain from making a prediction with some pre-defined cost. They focus on the predictor-rejector framework, which explicitly models the cost of abstention.
The key contributions are:

Counterexample showing that the score-based abstention formulation cannot achieve the Bayes solution in some natural settings, unlike the predictor-rejector formulation.

Negative results ruling out certain single-stage predictor-rejector surrogate losses.

New families of single-stage predictor-rejector surrogate losses for which they prove strong non-asymptotic and hypothesis set-specific consistency guarantees, resolving an open question.

Two-stage predictor-rejector formulations and their H-consistency bounds guarantees.

Realizable consistency guarantees for both single-stage and two-stage surrogate losses, resolving a recent open question.

Experiments on CIFAR-10, CIFAR-100 and SVHN datasets demonstrating the usefulness of the proposed surrogate losses.

Stats

The authors do not provide any specific numerical data or metrics in the content. The focus is on theoretical analysis and algorithm development.

Quotes

"We show in Section 3 that in some instances the optimal solution cannot be derived in the score-based formulation, unless we resort to more complex scoring functions. In contrast, the solution can be straightforwardly derived in the predictor-rejector formulation."
"We show in Section 3 that in some instances the optimal solution cannot be derived in the score-based formulation, unless we resort to more complex scoring functions. In contrast, the solution can be straightforwardly derived in the predictor-rejector formulation."

Key Insights Distilled From

Predictor-Rejector Multi-Class Abstention

by Anqi Mao,Meh... at arxiv.org 04-02-2024

https://arxiv.org/pdf/2310.14772.pdf

Deeper Inquiries

What are some real-world applications where the predictor-rejector formulation for multi-class abstention would be particularly useful compared to the score-based formulation

The predictor-rejector formulation for multi-class abstention can be particularly useful in real-world applications where the cost of making incorrect predictions is high, and the ability to abstain from making a prediction is crucial. One such application is in autonomous vehicle control systems, where incorrect predictions can lead to accidents and endanger lives. By incorporating abstention mechanisms using the predictor-rejector framework, the system can choose to abstain from making a prediction when the confidence in the prediction is low, thus potentially preventing dangerous situations.
Another application where the predictor-rejector formulation shines is in medical diagnosis systems. In scenarios where misdiagnosis can have severe consequences for patients, having the ability to abstain from providing a diagnosis can be essential. By using the predictor-rejector framework, the system can abstain from making a diagnosis when the confidence in the prediction is not high enough, reducing the risk of incorrect treatment decisions.

How can the theoretical guarantees provided for the single-stage and two-stage predictor-rejector surrogate losses be leveraged to design practical abstention algorithms for large-scale machine learning problems

The theoretical guarantees provided for the single-stage and two-stage predictor-rejector surrogate losses can be leveraged to design practical abstention algorithms for large-scale machine learning problems.
For the single-stage formulation, where the predictor and rejector are learned simultaneously, the guarantees of (H,R)-consistency bounds ensure that the surrogate losses are aligned with the abstention loss, leading to more accurate predictions and better decision-making on when to abstain. This can be applied in scenarios where real-time decision-making is crucial, such as in financial trading systems or fraud detection algorithms.
In the two-stage formulation, where the predictor is learned first and then the rejector is determined, the guarantees of realizable consistency provide assurance that the algorithm can effectively learn to abstain when necessary. This can be beneficial in applications where the predictor is already trained and retraining is not feasible, such as in image recognition systems or natural language processing tasks.
By utilizing these theoretical guarantees, practitioners can develop robust abstention algorithms that improve the reliability and accuracy of machine learning models in various domains.

Are there any other families of multi-class surrogate losses beyond the ones considered in this work that could satisfy the necessary conditions for (H,R)-consistency bounds in the predictor-rejector framework

While the families of multi-class surrogate losses considered in the work provide strong theoretical guarantees for (H,R)-consistency bounds in the predictor-rejector framework, there may be other families of losses that could also satisfy the necessary conditions. One potential family to explore could be the margin-based losses, similar to the hinge loss used in the work. These losses focus on the margin of confidence in predictions and could potentially align well with the predictor-rejector framework's requirements.
Additionally, exploring loss functions that incorporate uncertainty estimates or probabilistic predictions could be beneficial. Loss functions that take into account the uncertainty in predictions and the cost of incorrect decisions could provide a more nuanced approach to multi-class abstention. By considering the uncertainty in predictions, the algorithm can make more informed decisions on when to abstain, leading to improved performance in real-world applications.