Relaxed Quantile Regression: Prediction Intervals for Asymmetric Noise

2024-06-05

International Conference on Machine Learning

AI Summary

Conventional quantile regression requires prespecifying symmetric quantile levels, making it ill-suited for real-world scenarios with inherently asymmetric noise distributions; moreover, extending to multiple quantiles often inflates model complexity. Method: We propose Relaxed Quantile Regression (RQR), which eliminates rigid constraints on fixed quantiles and jointly optimizes prediction interval width and coverage probability within an empirical risk minimization framework—without distributional assumptions or parametric modeling. Contribution/Results: We provide finite-sample theoretical guarantees that RQR strictly achieves the target confidence level in coverage. Empirically, RQR significantly reduces average prediction interval width while maintaining exact nominal coverage, consistently outperforming both standard and multi-quantile quantile regression methods across diverse benchmarks.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

Constructing valid prediction intervals rather than point estimates is a well-established approach for uncertainty quantification in the regression setting. Models equipped with this capacity output an interval of values in which the ground truth target will fall with some prespecified probability. This is an essential requirement in many real-world applications where simple point predictions' inability to convey the magnitude and frequency of errors renders them insufficient for high-stakes decisions. Quantile regression is a leading approach for obtaining such intervals via the empirical estimation of quantiles in the (non-parametric) distribution of outputs. This method is simple, computationally inexpensive, interpretable, assumption-free, and effective. However, it does require that the specific quantiles being learned are chosen a priori. This results in (a) intervals that are arbitrarily symmetric around the median which is sub-optimal for realistic skewed distributions, or (b) learning an excessive number of intervals. In this work, we propose Relaxed Quantile Regression (RQR), a direct alternative to quantile regression based interval construction that removes this arbitrary constraint whilst maintaining its strengths. We demonstrate that this added flexibility results in intervals with an improvement in desirable qualities (e.g. mean width) whilst retaining the essential coverage guarantees of quantile regression.

Problem

• predicting intervals for skewed data
• improving quantile regression flexibility
• maintaining coverage guarantees in prediction

Innovation

• Relaxed Quantile Regression method
• Asymmetric noise handling
• Improved prediction intervals