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A Tutorial on Conformal Prediction

JournalofMachineLearningResearch9 (2008)371-421 Submitted8/07;Published3/08A TutorialonConformalPredictionGlennShafer CentreDepartmentofComputerScienceRoyalHo lloway, UniversityofLondonEgham,Surrey TW200EX,UKEditor:Sanjoy , togetherwitha methodthatmakesa Prediction yofa labely, it producesa setoflabels,typicallycontaining y, thatalsocontainsywithprobability1 .Conformalpredictioncanbeappliedtoany methodforproducing y: a nearest-neighbormethod,asupport-vectorma chine,ridgeregression, designedforanon-linesettinginwhichlabels arepredictedsucces-sively, eachonebeingrevealedbeforethenextis andvaluablefeatureofconformalpredictioni s thatif thesuccessive examplesaresampledindependentlyfromthesa medistribution,thenthesuccessive predictionswillberight1 ofthetime,eventhoughthey examplesaresampledindependently, treatmentofthetopicis providedinAlgorithmicLearningin a RandomWorld, byVladimirVovk,Alex Gammerman,andGlennShafer(Springer, 2005).

tically independent. This allows us to interpret “being right 95% of the time” in an unusually direct way. In §2.1, we illustrate this point with a well-worn example, normally distributed random vari-ables. In §2.2, we contrast confidence with full-fledged …

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