# MCNet: Monotonic Calibration Networks for Expressive Uncertainty Calibration in Online Advertising

arXiv: https://arxiv.org/abs/2503.00334 · HTML: https://mlsanity.com/paper/2503.00334/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 34 references that are in the map.
- First posted on arXiv 1 Mar 2025.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Deep & Cross Network for Ad Click Predictions](https://mlsanity.com/paper/1708.05123/) (2017)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)
- [Unconstrained Monotonic Neural Networks](https://mlsanity.com/paper/1908.05164/) (2019)
- [Deep Lattice Networks and Partial Monotonic Functions](https://mlsanity.com/paper/1709.06680/) (2017)
- [BARS: Towards Open Benchmarking for Recommender Systems](https://mlsanity.com/paper/2205.09626/) (2022)
- [Open Benchmarking for Click-Through Rate Prediction](https://mlsanity.com/paper/2009.05794/) (2020)
- [Field-aware Calibration: A Simple and Empirically Strong Method for Reliable Probabilistic Predictions](https://mlsanity.com/paper/1905.10713/) (2019)
- [A Generalized Doubly Robust Learning Framework for Debiasing Post-Click Conversion Rate Prediction](https://mlsanity.com/paper/2211.06684/) (2022)
- [Obtaining Calibrated Probabilities with Personalized Ranking Models](https://mlsanity.com/paper/2112.07428/) (2021)
- [Modeling Perception Errors towards Robust Decision Making in Autonomous Vehicles](https://mlsanity.com/paper/2001.11695/) (2020)
- [MBCT: Tree-Based Feature-Aware Binning for Individual Uncertainty Calibration](https://mlsanity.com/paper/2202.04348/) (2022)
- [Posterior Probability Matters: Doubly-Adaptive Calibration for Neural Predictions in Online Advertising](https://mlsanity.com/paper/2205.07295/) (2022)

## Built on by (most cited first, 1 of 1)

- [Conversion rate prediction in online advertising: modeling techniques, performance evaluation and future directions](https://mlsanity.com/paper/2512.01171/) (2025)

## Abstract (arXiv)

In online advertising, uncertainty calibration aims to adjust a ranking model's probability predictions to better approximate the true likelihood of an event, e.g., a click or a conversion. However, existing calibration approaches may lack the ability to effectively model complex nonlinear relations, consider context features, and achieve balanced performance across different data subsets. To tackle these challenges, we introduce a novel model called Monotonic Calibration Networks, featuring three key designs: a monotonic calibration function (MCF), an order-preserving regularizer, and a field-balance regularizer. The nonlinear MCF is capable of naturally modeling and universally approximating the intricate relations between uncalibrated predictions and the posterior probabilities, thus being much more expressive than existing methods. MCF can also integrate context features using a flexible model architecture, thereby achieving context awareness. The order-preserving and field-balance regularizers promote the monotonic relationship between adjacent bins and the balanced calibration performance on data subsets, respectively. Experimental results on both public and industrial datasets demonstrate the superior performance of our method in generating well-calibrated probability predictions.