platt scaling
**Platt Scaling** is a post-hoc calibration technique that transforms the raw output scores (logits) of a trained classifier into well-calibrated probabilities by fitting a logistic regression model on a held-out validation set. The method learns two parameters (slope A and intercept B) that map the original logit z to a calibrated probability p = 1/(1 + exp(Az + B)), effectively adjusting the model's confidence to match observed accuracy frequencies.
**Why Platt Scaling Matters in AI/ML:**
Platt scaling provides a **simple, effective method to convert overconfident or miscalibrated model outputs into reliable probability estimates** without retraining the original model, essential for decision-making systems that depend on accurate confidence scores.
• **Logistic transformation** — Platt scaling fits p(y=1|z) = σ(Az + B) where z is the model's raw score, A and B are learned on validation data to minimize negative log-likelihood; this two-parameter model corrects both scale (A) and bias (B) of the original scores
• **Post-hoc application** — The technique is applied after model training using a held-out calibration set, requiring no changes to model architecture, training procedure, or inference pipeline—just a thin calibration layer on top of existing outputs
• **Overconfidence correction** — Modern deep neural networks are systematically overconfident (predicted probability of 0.95 may have only 0.80 actual accuracy); Platt scaling compresses the probability range to match empirical accuracy, improving reliability
• **Binary to multiclass extension** — For multiclass classification, Platt scaling extends to temperature scaling (a single-parameter variant) or per-class Platt scaling; temperature scaling divides all logits by a learned temperature T before softmax
• **Validation set requirements** — Platt scaling requires a held-out calibration set (typically 1000-5000 examples) separate from both training and test sets; the calibration parameters are fit on this set using maximum likelihood
| Component | Specification | Notes |
|-----------|--------------|-------|
| Input | Raw logit or decision score z | From any trained classifier |
| Parameters | A (slope), B (intercept) | Learned on calibration set |
| Output | σ(Az + B) | Calibrated probability |
| Fitting | Max likelihood (NLL loss) | On held-out calibration data |
| Calibration Set Size | 1000-5000 examples | Separate from train and test |
| Multiclass Extension | Temperature scaling (T) | z_i/T before softmax |
| Computational Cost | Negligible | Two-parameter optimization |
**Platt scaling is the most widely used post-hoc calibration technique in machine learning, providing a simple two-parameter logistic transformation that converts miscalibrated model scores into reliable probability estimates, enabling trustworthy confidence-based decision making without any modification to the underlying model.**