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We develop conformal prediction methods for constructing valid predictiveconfidence sets in multiclass and multilabel problems without assumptions onthe data generating distribution. A challenge here is that typical conformalprediction methods---which give marginal validity (coverage)guarantees---provide uneven coverage, in that they address easy examples at theexpense of essentially ignoring difficult examples. By leveraging ideas fromquantile regression, we build methods that always guarantee correct coveragebut additionally provide (asymptotically optimal) conditional coverage for bothmulticlass and multilabel prediction problems. To address the potentialchallenge of exponentially large confidence sets in multilabel prediction, webuild tree-structured classifiers that efficiently account for interactionsbetween labels. Our methods can be bolted on top of any classificationmodel---neural network, random forest, boosted tree---to guarantee itsvalidity. We also provide an empirical evaluation, simultaneously providing newvalidation methods, that suggests the more robust coverage of our confidencesets.

Knowing what you know: valid and validated confidence sets in multiclass and multilabel prediction