Unconstrained Monotonic Calibration of Predictions in Deep Ranking Systems

Ranking models primarily focus on modeling the relative order of predictions while often neglecting the significance of the accuracy of their absolute values. However, accurate absolute values are essential for certain downstream tasks, necessitating the calibration of the original predictions. To address this, existing calibration approaches typically employ predefined transformation functions with order-preserving properties to adjust the original predictions. Unfortunately, these functions often adhere to fixed forms, such as piece-wise linear functions, which exhibit limited expressiveness and flexibility, thereby constraining their effectiveness in complex calibration scenarios. To mitigate this issue, we propose implementing a calibrator using an Unconstrained Monotonic Neural Network (UMNN), which can learn arbitrary monotonic functions with great modeling power. This approach significantly relaxes the constraints on the calibrator, improving its flexibility and expressiveness while avoiding excessively distorting the original predictions by requiring monotonicity. Furthermore, to optimize this highly flexible network for calibration, we introduce a novel additional loss function termed Smooth Calibration Loss (SCLoss), which aims to fulfill a necessary condition for achieving the ideal calibration state. Extensive offline experiments confirm the effectiveness of our method in achieving superior calibration performance. Moreover, deployment in Kuaishou's large-scale online video ranking system demonstrates that the method's calibration improvements translate into enhanced business metrics. The source code is available atthis https URL.

@article{bai2025_2504.14243,
  title={ Unconstrained Monotonic Calibration of Predictions in Deep Ranking Systems },
  author={ Yimeng Bai and Shunyu Zhang and Yang Zhang and Hu Liu and Wentian Bao and Enyun Yu and Fuli Feng and Wenwu Ou },
  journal={arXiv preprint arXiv:2504.14243},
  year={ 2025 }
}