Regression Conformal Prediction under Bias

Abstract: Uncertainty quantification is crucial to account for the imperfect predictions of machine learning algorithms for high-impact applications. Conformal prediction (CP) is a powerful framework for uncertainty quantification that generates calibrated prediction intervals with valid coverage. In this work, we study how CP intervals are affected by bias - the systematic deviation of a prediction from ground truth values - a phenomenon prevalent in many real-world applications. We investigate the influence of bias on interval lengths of two different types of adjustments -- symmetric adjustments, the conventional method where both sides of the interval are adjusted equally, and asymmetric adjustments, a more flexible method where the interval can be adjusted unequally in positive or negative directions. We present theoretical and empirical analyses characterizing how symmetric and asymmetric adjustments impact the "tightness" of CP intervals for regression tasks. Specifically for absolute residual and quantile-based non-conformity scores, we prove: 1) the upper bound of symmetrically adjusted interval lengths increases by $2|b|$ where $b$ is a globally applied scalar value representing bias, 2) asymmetrically adjusted interval lengths are not affected by bias, and 3) conditions when asymmetrically adjusted interval lengths are guaranteed to be smaller than symmetric ones. Our analyses suggest that even if predictions exhibit significant drift from ground truth values, asymmetrically adjusted intervals are still able to maintain the same tightness and validity of intervals as if the drift had never happened, while symmetric ones significantly inflate the lengths. We demonstrate our theoretical results with two real-world prediction tasks: sparse-view computed tomography (CT) reconstruction and time-series weather forecasting. Our work paves the way for more bias-robust machine learning systems.

• The paper presents robust theoretical and empirical findings that reveal symmetric prediction intervals inflate with bias, while asymmetric adjustments maintain interval tightness.
• It validates its claims through real-world examples in CT reconstruction and weather forecasting, demonstrating the practical relevance of bias-aware prediction methods.
• Results suggest that employing asymmetric CP adjustments can enhance prediction reliability in high-stakes applications by effectively mitigating the impact of bias.

Analyzing the Impact of Bias in Regression Conformal Prediction

The paper "Regression Conformal Prediction under Bias" by Cheung et al. explores the pivotal topic of uncertainty quantification in machine learning, with a particular focus on Conformal Prediction (CP) applied to regression tasks. The study prioritizes understanding how CP intervals are influenced by prediction bias—a common issue in real-world applications where predictive models deviate systematically from ground truths.

Key Contributions

This comprehensive work contrasts symmetric and asymmetric adjustments in CP, examining their effectiveness under the duress of biased predictions:

1. Theoretical and Empirical Insights: The authors present robust theoretical findings complemented by empirical examples. They prove that symmetric interval lengths are directly affected by bias, showing that their upper bounds inflate by a factor of $2|b|$, where $b$ signifies the bias magnitude. Conversely, asymmetric adjustments maintain interval length independently of bias.
2. Empirical Validation: The paper supports theoretical assertions through empirical analysis of two real-world prediction tasks: sparse-view computed tomography (CT) reconstruction and weather forecasting. This practical evaluation underscores the proposed model’s relevance in bias-prone environments.
3. Tightness of Asymmetric Adjustments: Asymmetric intervals continually offer smaller lengths compared to symmetric ones when a clear bias exists. The study delineates specific conditions under which the asymmetric method unequivocally outperforms its symmetric counterpart in terms of interval tightness.

Implications and Future Directions

Practical Implications

The results suggest that in scenarios where machine learning models exhibit bias due to factors like sensor drift or concept drift, employing asymmetric adjustments in CP can yield more reliable and compact prediction intervals. This finding holds particular significance in high-stakes fields such as medical imaging and weather prediction, where prediction accuracy and efficiency are paramount.

Theoretical Contributions

The theoretical framework posed by the authors enriches the understanding of CP in biased settings. By formalizing the relationship between bias and interval adjustments, the paper equips researchers with a new perspective on ensuring the validity and compactness of prediction intervals, regardless of the biases present.

Speculation on Future Developments

Looking forward, this research opens pathways to further investigate how CP can be extended and adapted to accommodate other types of biases, including those localization-specific or temporal. Additionally, exploring the integration of adaptive, bias-aware mechanisms in CP could improve model robustness and predictive accuracy even further.

Conclusion

Cheung et al.'s exploration into bias-aware regression conformal prediction advances our understanding of uncertainty quantification's robustness in machine learning. By proving that asymmetric adjustments mitigate bias effects and provide tighter intervals, the study lays the groundwork for designing more bias-resilient predictive systems. This work is a profound step toward enhancing the reliability and applicability of CP in varied contexts, especially where prediction precision cannot be compromised.