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Theoretically Grounded Loss Functions and Algorithms for Efficient Multi-Class Abstention


Core Concepts
The authors introduce new families of surrogate losses for the multi-class abstention loss function, including state-of-the-art surrogate losses in the single-stage setting and a novel family of loss functions in the two-stage setting. They prove strong non-asymptotic and hypothesis set-specific consistency guarantees for these surrogate losses, which upper-bound the estimation error of the abstention loss function in terms of the estimation error of the surrogate loss.
Abstract
The paper analyzes the score-based formulation of learning with abstention in the multi-class classification setting. The authors introduce new families of surrogate losses for the abstention loss function, which include the state-of-the-art surrogate losses in the single-stage setting and a novel family of loss functions in the two-stage setting. For the single-stage setting, the authors prove strong non-asymptotic and hypothesis set-specific consistency guarantees for these surrogate losses, which upper-bound the estimation error of the abstention loss function in terms of the estimation error of the surrogate loss. These guarantees are more favorable than the existing asymptotic consistency guarantees. For the two-stage setting, the authors propose surrogate losses and prove that they benefit from similar strong consistency guarantees. They show that the two-stage formulation is also realizable H-consistent, which addresses an open problem in the literature. The authors experimentally evaluate their new algorithms on CIFAR-10, CIFAR-100, and SVHN datasets and demonstrate the practical significance of their new surrogate losses and two-stage abstention algorithms. The results also show that the relative performance of the state-of-the-art score-based surrogate losses can vary across datasets.
Stats
The authors use the following datasets in their experiments: CIFAR-10 CIFAR-100 SVHN
Quotes
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Deeper Inquiries

How can the proposed two-stage score-based abstention algorithms be extended to other multi-class classification tasks beyond the standard image classification setting

The proposed two-stage score-based abstention algorithms can be extended to other multi-class classification tasks beyond the standard image classification setting by adapting the algorithm to suit the specific characteristics of the new tasks. For example, in natural language processing tasks such as sentiment analysis or text classification, the first stage of the algorithm could involve training a language model to predict the sentiment or category of a given text. The second stage could then focus on determining when to abstain from providing a prediction based on the confidence of the language model's output. By adjusting the surrogate losses and the hypothesis sets to align with the requirements of the new tasks, the two-stage formulation can be effectively applied to a wide range of multi-class classification problems.

What are the potential limitations or drawbacks of the two-stage formulation compared to the single-stage formulation, and under what conditions would the single-stage formulation be preferable

One potential limitation of the two-stage formulation compared to the single-stage formulation is the increased complexity and computational cost associated with training two separate models. The need to train a predictor in the first stage and then optimize the abstention decision in the second stage can lead to longer training times and higher resource requirements. Additionally, coordinating the training of two models and ensuring their compatibility can be challenging. The single-stage formulation may be preferable in scenarios where computational resources are limited, and a simpler approach is sufficient to achieve the desired performance. If the dataset is relatively small or the task is not highly complex, a single-stage model may provide adequate results without the added complexity of a two-stage approach. Furthermore, in situations where real-time decision-making is crucial, the single-stage formulation may be more suitable due to its streamlined process.

The authors highlight the varying relative performance of the state-of-the-art cross-entropy score-based surrogate losses across datasets. What factors or dataset characteristics might contribute to these performance differences, and how can this insight guide the selection of appropriate surrogate losses for different application domains

The varying relative performance of the state-of-the-art cross-entropy score-based surrogate losses across datasets can be influenced by several factors. One key factor is the distribution of the data within each dataset, as the balance and separability of the classes can impact the effectiveness of different surrogate losses. Additionally, the complexity and diversity of the classes in the dataset can play a role in determining which surrogate loss performs best. Furthermore, the presence of outliers or noisy data points in certain datasets may affect the performance of the surrogate losses, as they may respond differently to data irregularities. The nature of the task and the specific requirements of the application domain can also influence the choice of surrogate loss, as different losses may prioritize different aspects of the classification problem. By understanding these factors and analyzing the performance of surrogate losses across different datasets, researchers and practitioners can make informed decisions about selecting the most appropriate surrogate loss for a given application domain. This insight can guide the development of more effective algorithms and improve the overall performance of multi-class abstention systems.
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