Platt Scaling

Platt scaling is a method for turning a model's raw scores into probabilities you can actually trust. Many classifiers output a number that ranks cases correctly — higher means more likely positive — but that number is not a true probability. A support vector machine or a boosted-tree model might emit a 0.9 for a case that is really only 60 percent likely to be positive. Platt scaling fixes this by fitting a logistic (sigmoid) curve that maps each raw score to a calibrated probability, using a held-out set of examples where the real outcomes are known. The fit has only a couple of parameters, so it is simple and stable. The technique is named for John Platt, who introduced it for support vector machines in 1999.

Calibration matters because most decisions are made on probabilities, not rankings. You set a threshold, compute an expected value, size a bid, or split a budget — all of which assume that a predicted 0.3 really does convert about 30 percent of the time. A model can have excellent discrimination, meaning it ranks cases beautifully and scores a high AUC, yet be badly calibrated, saying 70 percent when the truth is 40 percent. Discrimination and calibration are separate qualities, and a strong AUC does not guarantee honest probabilities. Platt scaling repairs calibration without disturbing the ranking, since a monotonic sigmoid preserves the order of scores. That makes it a cheap, effective step to run after training whenever the downstream use depends on the probability itself and not merely the rank.

Platt scaling has a well-known cousin, isotonic regression, and choosing between them is mostly a question of shape and data. Platt scaling assumes the miscalibration follows a sigmoid: it fits that specific logistic curve and nothing else. Because it has so few parameters, it needs very little calibration data and rarely overfits, but it is only correct when the true relationship between score and probability genuinely resembles a sigmoid. Isotonic regression makes no such assumption. It fits any monotonically increasing step function from scores to probabilities, so it can correct odd, non-sigmoidal distortions that Platt scaling cannot. That flexibility is powerful but hungry — isotonic regression needs more data and can overfit on small held-out sets, producing a jagged, unreliable mapping.

The practical guidance falls out of that contrast. Reach for Platt scaling when your calibration set is small or when the miscalibration looks roughly sigmoidal, which is common for margin-based models like support vector machines. Reach for isotonic regression when you have plenty of held-out data and suspect the distortion is more complex than a single S-curve. Both methods preserve the model's ranking, so neither changes which cases score higher than which — they only remap the scores onto the probability scale. The difference is entirely flexibility versus data appetite. A common mistake is to default to isotonic regression on a tiny validation set and end up with an overfit calibration that is worse than the simple sigmoid would have been.

Using Platt scaling well starts with clean data hygiene: fit the calibration curve on a held-out set that the model never saw during training, because calibrating on the training data gives an optimistic mapping that falls apart in production. Check the result with a reliability diagram, which plots predicted probability against observed frequency — a well-calibrated model hugs the diagonal — and with a summary metric such as the Brier score or log loss, both of which reward honest probabilities. Treat calibration as something that decays: when the input data drifts and the world changes, the mapping that was accurate months ago drifts with it, so recalibrate on fresh data rather than assuming the fit is permanent.

The failures are specific and avoidable. People calibrate on training data and mistake the resulting optimism for success. They apply Platt scaling when the miscalibration is not sigmoidal, forcing an S-curve onto a relationship that does not have one. They confuse a strong AUC with good calibration and never check whether the probabilities are honest at all. And they fit the calibration once and forget it, letting drift silently degrade the mapping. The discipline is to calibrate on held-out data, verify with a reliability diagram and a proper scoring rule, choose Platt scaling when its sigmoid assumption fits and the data is limited, and recalibrate whenever the distribution moves.

Named for researcher John Platt, who introduced the sigmoid-fitting calibration method for support vector machines in 1999.

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