← ISOM 835 · Session 9
Interactive · Intervals That Keep Their Promise

The Conformal Explorer

A model predicts a house price (or a demand, or a delivery time). A point forecast is a bet. Split conformal prediction measures the model's errors on a calibration set it never trained on, takes the 90th-percentile error, and wraps every new prediction in a band that wide. The promise: over many new cases, about 90% land inside — for any model, with no assumption about the error shape. Test the promise.

Prediction band on new cases
Calibration casesNew cases (the test of the promise)Model predictionConformal band
hover a new case to see whether it landed inside the band
Calibration residuals |y − ŷ|
residualsthe quantile that sets the band
Coverage over repeated draws of new data
coverage per drawtarget
The promise, checked
—
Target coverage—
Band half-width (quantile of residuals)—
New cases inside / total—
Mean coverage over repeats—

The recipe: fit the model on training data; compute residuals rᵢ = |yᵢ − ŷᵢ| on a separate calibration set of n cases; take q = the ⌈(n+1)(1−α)⌉-th smallest residual; predict ŷ ± q for every new case. Coverage ≥ 1−α is guaranteed on average as long as new cases are exchangeable with the calibration cases — which is exactly what breaks under distribution shift. A bad model gets wide bands, not broken promises. In MAPIE this is SplitConformalRegressor.