Transcription of A Tutorial on Conformal Prediction
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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).
SHAFER AND VOVK region—a set Γ0:05 that contains y with probability at least 95%. Typically Γ0:05 also contains the prediction yˆ. We call yˆ the point prediction, and we call Γ0:05 the region prediction. In the case of regression, where y is a number, Γ0:05 is typically an interval around yˆ. In the case of classification,
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