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In a supervised learning problem, given a predicted value that is the outputof some trained model, how can we quantify our uncertainty around thisprediction? Distribution-free predictive inference aims to construct predictionintervals around this output, with valid coverage that does not rely onassumptions on the distribution of the data or the nature of the model trainingalgorithm. Existing methods in this area, including conformal prediction andjackknife+, offer theoretical guarantees that hold marginally (i.e., on averageover a draw of training and test data). In contrast, training-conditionalcoverage is a stronger notion of validity that ensures predictive coverage ofthe test point for most draws of the training data, and is thus a moredesirable property in practice. Training-conditional coverage was shown by Vovk[2012] to hold for the split conformal method, but recent work by Bian andBarber [2023] proves that such validity guarantees are not possible for thefull conformal and jackknife+ methods without further assumptions. In thispaper, we show that an assumption of algorithmic stability ensures that thetraining-conditional coverage property holds for the full conformal andjackknife+ methods.

Algorithmic stability implies training-conditional coverage for distribution-free prediction methods