Conformal Risk Control for Ordinal Classification: Developing Tailored Loss Functions and Algorithms to Quantify Uncertainty in Ordinal Prediction Tasks

Core Concepts

The authors develop conformal risk control methods specifically for ordinal classification tasks, introducing two types of loss functions (weight-based and divergence-based) and corresponding algorithms to construct optimal prediction sets that control the expected risk at a desired level.

Abstract

The authors address the problem of efficiently processing and analyzing content for insights, focusing on ordinal classification tasks. They formulate the ordinal classification problem within the conformal risk control framework and provide theoretical risk bounds for the proposed risk control method.
The key highlights are:

Formulation of the ordinal classification task in the conformal risk control framework, with three conditions for an ideal prediction set in the ordinal setting.
Provision of upper and lower bounds of risk for the proposed risk control method.
Proposal of two different types of loss functions (weight-based and divergence-based) for constructing prediction sets in the ordinal classification setting, and development of corresponding algorithms to find the optimal prediction sets.
Demonstration of the effectiveness of the proposed methods on both simulated and real-world datasets (UTKFace and diabetic retinopathy detection), and analysis of the differences between the two types of risks.

The authors show that the proposed algorithms can effectively control the expected risk at a desired level, while satisfying the specific requirements of ordinal classification tasks. The weight-based risk is more suitable for adjusting the importance of certain classes, while the divergence-based risk is more suitable for cases where large prediction errors are of greater concern.

Stats

The simulated ordinal data has 10 classes, with 2,000 data points per class.
The UTKFace dataset has over 20,000 face images with age annotations, which are discretized into 20 age groups.
The diabetic retinopathy detection dataset has over 35,000 retina images with clinician ratings on the presence of diabetic retinopathy, ranging from 0 (no DR) to 4 (proliferative DR).

Quotes

"Conformal risk control generalizes the miscoverage rate to any bounded non-increasing loss functions, which offers a lot of flexibility to problems where other metrics are valued over the miscoverage rate."
"In an actual ordinal classification problem, different classes may have different importance and large prediction errors are often more concerned."

Key Insights Distilled From

Conformal Risk Control for Ordinal Classification

by Yunpeng Xu,W... at arxiv.org 05-02-2024

https://arxiv.org/pdf/2405.00417.pdf

Deeper Inquiries

How do the weight functions impact the conditional coverage for each individual class in the ordinal classification setting

In the ordinal classification setting, the weight functions impact the conditional coverage for each individual class by assigning different weights to each class based on their importance. These weight functions influence the prediction sets by adjusting the significance of each class in the risk calculation. For example, weight functions that assign higher weights to certain classes will prioritize those classes in the prediction sets, ensuring that the risk control is tailored to the specific characteristics of the problem. By adjusting the weights, the conditional coverage for each class can be customized to reflect the relative importance of different classes in the ordinal classification task.

How can one choose the appropriate weight function and risk threshold for a specific ordinal classification problem

Choosing the appropriate weight function and risk threshold for a specific ordinal classification problem involves understanding the characteristics of the data and the objectives of the prediction task. To select the right weight function, one should consider the relative importance of different classes in the ordinal classification problem. For instance, if certain classes are more critical than others, assigning higher weights to those classes can ensure that the prediction sets prioritize them accordingly. The risk threshold should be chosen based on the desired level of confidence in the predictions and the tolerance for prediction errors. By adjusting the weight function and risk threshold, one can tailor the conformal risk control method to the specific requirements of the ordinal classification problem.

What other types of loss functions or distance measures could be explored for ordinal conformal risk control, and how would they affect the resulting prediction sets

Other types of loss functions or distance measures that could be explored for ordinal conformal risk control include asymmetric loss functions, weighted loss functions based on class frequencies, and distance measures that capture the ordinal nature of the classes. Asymmetric loss functions can penalize prediction errors differently based on the direction of the error, reflecting the ordinal relationship among classes. Weighted loss functions based on class frequencies can adjust the loss calculation to account for imbalanced class distributions. Distance measures that consider the ordinal structure of the classes, such as the absolute difference between class labels or custom distance metrics tailored to the ordinal classification problem, can provide a more nuanced evaluation of prediction errors. Exploring these alternative loss functions and distance measures can offer insights into different aspects of the ordinal classification task and how they impact the resulting prediction sets.