Distribution-free binary classification: prediction sets, confidence
intervals and calibration
- URL: http://arxiv.org/abs/2006.10564v4
- Date: Wed, 16 Feb 2022 18:42:02 GMT
- Title: Distribution-free binary classification: prediction sets, confidence
intervals and calibration
- Authors: Chirag Gupta, Aleksandr Podkopaev, Aaditya Ramdas
- Abstract summary: We study three notions of uncertainty quantification -- calibration, confidence intervals and prediction sets -- for binary classification in the distribution-free setting.
We derive confidence intervals for binned probabilities for both fixed-width and uniform-mass binning.
As a consequence of our 'tripod' theorems, these confidence intervals for binned probabilities lead to distribution-free calibration.
- Score: 106.50279469344937
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study three notions of uncertainty quantification -- calibration,
confidence intervals and prediction sets -- for binary classification in the
distribution-free setting, that is without making any distributional
assumptions on the data. With a focus towards calibration, we establish a
'tripod' of theorems that connect these three notions for score-based
classifiers. A direct implication is that distribution-free calibration is only
possible, even asymptotically, using a scoring function whose level sets
partition the feature space into at most countably many sets. Parametric
calibration schemes such as variants of Platt scaling do not satisfy this
requirement, while nonparametric schemes based on binning do. To close the
loop, we derive distribution-free confidence intervals for binned probabilities
for both fixed-width and uniform-mass binning. As a consequence of our 'tripod'
theorems, these confidence intervals for binned probabilities lead to
distribution-free calibration. We also derive extensions to settings with
streaming data and covariate shift.
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