# MBCT: Tree-Based Feature-Aware Binning for Individual Uncertainty Calibration

arXiv: https://arxiv.org/abs/2202.04348 · HTML: https://mlsanity.com/paper/2202.04348/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 26 references that are in the map.
- First posted on arXiv 9 Feb 2022.

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

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Deep Interest Evolution Network for Click-Through Rate Prediction](https://mlsanity.com/paper/1809.03672/) (2018)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Mitigating Bias in Calibration Error Estimation](https://mlsanity.com/paper/2012.08668/) (2020)
- [Distribution-free binary classification: prediction sets, confidence intervals and calibration](https://mlsanity.com/paper/2006.10564/) (2020)
- [Budget Constrained Bidding by Model-free Reinforcement Learning in Display Advertising](https://mlsanity.com/paper/1802.08365/) (2018)
- [Individual Calibration with Randomized Forecasting](https://mlsanity.com/paper/2006.10288/) (2020)
- [Joint Optimization of Tree-based Index and Deep Model for Recommender Systems](https://mlsanity.com/paper/1902.07565/) (2019)
- [Bid Optimization by Multivariable Control in Display Advertising](https://mlsanity.com/paper/1905.10928/) (2019)
- [Learning for Single-Shot Confidence Calibration in Deep Neural Networks through Stochastic Inferences](https://mlsanity.com/paper/1809.10877/) (2018)
- [Attended Temperature Scaling: A Practical Approach for Calibrating Deep Neural Networks](https://mlsanity.com/paper/1810.11586/) (2018)
- [Binary Classifier Calibration: Non-parametric approach](https://mlsanity.com/paper/1401.3390/) (2014)

## Built on by (most cited first, 11 of 11)

- [Posterior Probability Matters: Doubly-Adaptive Calibration for Neural Predictions in Online Advertising](https://mlsanity.com/paper/2205.07295/) (2022)
- [Capturing Conversion Rate Fluctuation during Sales Promotions: A Novel Historical Data Reuse Approach](https://mlsanity.com/paper/2305.12837/) (2023)
- [Adaptive Neural Ranking Framework: Toward Maximized Business Goal for Cascade Ranking Systems](https://mlsanity.com/paper/2310.10462/) (2023)
- [Deep Ensemble Shape Calibration: Multi-Field Post-hoc Calibration in Online Advertising](https://mlsanity.com/paper/2401.09507/) (2024)
- [Confidence-Aware Multi-Field Model Calibration](https://mlsanity.com/paper/2402.17655/) (2024)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [GETS: Ensemble Temperature Scaling for Calibration in Graph Neural Networks](https://mlsanity.com/paper/2410.09570/) (2024)
- [Scaling Laws for Online Advertisement Retrieval](https://mlsanity.com/paper/2411.13322/) (2024)
- [Learning Cascade Ranking as One Network](https://mlsanity.com/paper/2503.09492/) (2025)
- [MCNet: Monotonic Calibration Networks for Expressive Uncertainty Calibration in Online Advertising](https://mlsanity.com/paper/2503.00334/) (2025)
- [LDACP: Long-Delayed Ad Conversions Prediction Model for Bidding Strategy](https://mlsanity.com/paper/2411.16095/) (2024)

## Abstract (arXiv)

Most machine learning classifiers only concern classification accuracy, while certain applications (such as medical diagnosis, meteorological forecasting, and computation advertising) require the model to predict the true probability, known as a calibrated estimate. In previous work, researchers have developed several calibration methods to post-process the outputs of a predictor to obtain calibrated values, such as binning and scaling methods. Compared with scaling, binning methods are shown to have distribution-free theoretical guarantees, which motivates us to prefer binning methods for calibration. However, we notice that existing binning methods have several drawbacks: (a) the binning scheme only considers the original prediction values, thus limiting the calibration performance; and (b) the binning approach is non-individual, mapping multiple samples in a bin to the same value, and thus is not suitable for order-sensitive applications. In this paper, we propose a feature-aware binning framework, called Multiple Boosting Calibration Trees (MBCT), along with a multi-view calibration loss to tackle the above issues. Our MBCT optimizes the binning scheme by the tree structures of features, and adopts a linear function in a tree node to achieve individual calibration. Our MBCT is non-monotonic, and has the potential to improve order accuracy, due to its learnable binning scheme and the individual calibration. We conduct comprehensive experiments on three datasets in different fields. Results show that our method outperforms all competing models in terms of both calibration error and order accuracy. We also conduct simulation experiments, justifying that the proposed multi-view calibration loss is a better metric in modeling calibration error.