Summary  
This chapter covers methods for calibrating classifiers’ probability outputs by comparing Platt scaling, isotonic regression, and histogram binning.  

General domain of usage  
Machine learning classification

When you compare **Platt scaling**, **isotonic regression**, and **histogram binning**, you are looking at three widely used methods for calibrating probabilistic outputs of classifiers. Each method has a unique approach and underlying assumptions:

- **Platt scaling** fits a **logistic regression** model to the classifier's scores, transforming them into calibrated probabilities. This method assumes a **sigmoidal (S-shaped) relationship** between the uncalibrated scores and the true probabilities;
- **Isotonic regression** is a **non-parametric** method that fits a free-form, monotonically increasing function to the scores. It does not assume any specific shape, making it more flexible but potentially prone to overfitting, especially on small datasets;
- **Histogram binning** divides the predicted scores into discrete bins and assigns the average observed frequency of the positive class within each bin as the calibrated probability. This method is simple and interpretable, but the choice of bin count can affect performance and calibration quality.

Understanding these differences is crucial for selecting the right calibration method for your data and use case.

Which calibration method is most likely to overfit on small datasets?

Which calibration method assumes a sigmoidal relationship between uncalibrated scores and true probabilities?

Master the principles and practical techniques for measuring, interpreting, and improving the probabilistic calibration of machine learning models. Learn to use reliability diagrams, calibration metrics, and modern calibration methods to ensure your models produce trustworthy probability estimates.

Explore the core concepts of model calibration, including the meaning of calibration, visual tools for assessment, and key quantitative metrics.

Apply and compare practical calibration techniques, and evaluate their effects on different models.

Explore real-world calibration scenarios, method selection, stability assessment, and end-to-end workflows.

Comparing Calibration Methods

1. Which calibration method is most likely to overfit on small datasets?

2. Which calibration method assumes a sigmoidal relationship between uncalibrated scores and true probabilities?