Online Multivalid Learning: Means, Moments, and Prediction Intervals

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dc.citation.articleNumber82en_US
dc.citation.journalTitle13th Innovations in Theoretical Computer Science Conference (ITCS 2022)en_US
dc.contributor.authorGupta, Varunen_US
dc.contributor.authorJung, Christopheren_US
dc.contributor.authorNoarov, Georgyen_US
dc.contributor.authorPai, Mallesh M.en_US
dc.contributor.authorRoth, Aaronen_US
dc.date.accessioned2022-03-24T13:31:34Zen_US
dc.date.available2022-03-24T13:31:34Zen_US
dc.date.issued2022en_US
dc.description.abstractWe present a general, efficient technique for providing contextual predictions that are “multivalid” in various senses, against an online sequence of adversarially chosen examples (x, y). This means that the resulting estimates correctly predict various statistics of the labels y not just marginally –as averaged over the sequence of examples – but also conditionally on x ∈ G for any G belonging to an arbitrary intersecting collection of groups G. We provide three instantiations of this framework. The first is mean prediction, which corresponds to an online algorithm satisfying the notion of multicalibration from [5]. The second is variance and higher moment prediction, which corresponds to an online algorithm satisfying the notion of mean-conditioned moment multicalibration from [6]. Finally, we define a new notion of prediction interval multivalidity, and give an algorithm for finding prediction intervals which satisfy it. Because our algorithms handle adversarially chosen examples, they can equally well be used to predict statistics of the residuals of arbitrary point prediction methods, giving rise to very general techniques for quantifying the uncertainty of predictions of black box algorithms, even in an online adversarial setting. When instantiated for prediction intervals, this solves a similar problem as conformal prediction, but in an adversarial environment and with multivalidity guarantees stronger than simple marginal coverage guarantees.en_US
dc.identifier.citationGupta, Varun, Jung, Christopher, Noarov, Georgy, et al.. "Online Multivalid Learning: Means, Moments, and Prediction Intervals." <i>13th Innovations in Theoretical Computer Science Conference (ITCS 2022),</i> (2022) Dagstuhl Publishing: https://doi.org/10.4230/LIPIcs.ITCS.2022.82.en_US
dc.identifier.digitalLIPIcs-ITCS-2022-82en_US
dc.identifier.doihttps://doi.org/10.4230/LIPIcs.ITCS.2022.82en_US
dc.identifier.urihttps://hdl.handle.net/1911/112031en_US
dc.language.isoengen_US
dc.publisherDagstuhl Publishingen_US
dc.rightsLicensed under Creative Commons License CC-BY 4.0en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.titleOnline Multivalid Learning: Means, Moments, and Prediction Intervalsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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