Conformal Prediction
Description
Conformal prediction wraps any trained model so that, instead of a single answer, it returns a set of plausible answers (an interval, for a numeric prediction) that contains the true outcome at a chosen rate, such as at least 95% of the time. It first scores, on a calibration set of labelled data kept apart from training, how unusual each known outcome looks given the model's prediction, using a nonconformity score, and for a new case it keeps every candidate answer whose score falls below a threshold taken from those calibration scores. A diagnostic model might then return 'cancer or benign tumour' rather than 'likely cancer', and with a suitable score the sets grow larger where the model is less certain. The guarantee is distribution-free, meaning it assumes nothing about the shape of the data, but it does assume the calibration data and new cases are exchangeable, roughly that they come from the same source in no particular order. It holds on average over all cases, not within each subgroup, unless the calibration is done separately within each predefined group (Mondrian conformal prediction), which needs enough calibration cases in every group.
Example Use Cases
Reliability
A medicinal chemistry team screening compounds in silico builds prediction sets of the protein targets each compound may be active against, at 95% coverage. Compounds with a single-target set go to lab testing for that target, and those with several targets go to a wider panel, so costly experiments follow how uncertain the model is.
Transparency
Providing transparent multi-class predictions in judicial risk assessment by showing all plausible risk categories at the stated coverage level, enabling judges to see the full range of possibilities rather than just a single point estimate.
Fairness
A university predicts whether first-year students will complete their degree and offers early support when the 90% prediction set includes 'withdraws'. To keep that 90% true for every group, not only on average, the data team calibrates the sets separately within each demographic group, then checks coverage and average set size per group on held-out students. A group with too few calibration cases is reported as not covered by the guarantee.
Limitations
- Sets can be wide enough to be useless. A multi-class set holding most classes, or an interval spanning the plausible range, meets the coverage target but tells the decision-maker little, and sets containing opposing outcomes make decisions hard. Width depends on the model's quality and the scoring rule chosen, and the guarantee says nothing about it.
- Needs labelled calibration data kept apart from training. On small datasets that means less data to train on, or a coarse and unstable coverage level, and variants that avoid a separate calibration set need several model fits.
- The guarantee assumes calibration data and new cases are exchangeable, roughly that they come from the same source in no particular order. Drift, a changed population or strongly time-ordered data break it, and coverage then falls below target with no warning. In Shafer and Vovk's example, a nominal 5% error rate rose to 8% on a systematically different test set.
- Coverage is guaranteed on average over all cases, not for each individual or subgroup, so a model can reach 95% overall while covering a minority group far less often. Mondrian calibration fixes this only for predefined, non-overlapping groups. It needs each new case's group at prediction time and is unstable when a group has few calibration cases (MAPIE's tutorial gives under 200 as an example).
- Cost depends on the variant. Split conformal prediction adds little beyond scoring a held-out set, but full conformal prediction re-evaluates every candidate outcome and cross-conformal variants refit the model several times, which can be prohibitive for large models or real-time use.
Resources
Research Papers
A tutorial on conformal prediction
Conformal prediction uses past experience to determine precise levels of confidence in new predictions. Given an error probability $ε$, together with a method that makes a prediction $\hat{y}$ of a label $y$, it produces a set of labels, typically containing $\hat{y}$, that also contains $y$ with probability $1-ε$. Conformal prediction can be applied to any method for producing $\hat{y}$: a nearest-neighbor method, a support-vector machine, ridge regression, etc. Conformal prediction is designed for an on-line setting in which labels are predicted successively, each one being revealed before the next is predicted. The most novel and valuable feature of conformal prediction is that if the successive examples are sampled independently from the same distribution, then the successive predictions will be right $1-ε$ of the time, even though they are based on an accumulating dataset rather than on independent datasets. In addition to the model under which successive examples are sampled independently, other on-line compression models can also use conformal prediction. The widely used Gaussian linear model is one of these. This tutorial presents a self-contained account of the theory of conformal prediction and works through several numerical examples. A more comprehensive treatment of the topic is provided in "Algorithmic Learning in a Random World", by Vladimir Vovk, Alex Gammerman, and Glenn Shafer (Springer, 2005).