Honest calibration assessment for binary outcome predictions
Summary Probability predictions from binary regressions or machine learning methods ought to be calibrated: if an event is predicted to occur with probability $x$, it should materialize with approximately that frequency, which means that the so-called calibration curve $p(\cdot)$ should equal the id...
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Veröffentlicht in: | Biometrika 2023-09, Vol.110 (3), p.663-680 |
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creator | Dimitriadis, Timo Dümbgen, Lutz Henzi, Alexander Puke, Marius Ziegel, Johanna |
description | Summary
Probability predictions from binary regressions or machine learning methods ought to be calibrated: if an event is predicted to occur with probability $x$, it should materialize with approximately that frequency, which means that the so-called calibration curve $p(\cdot)$ should equal the identity, i.e., $p(x) = x$ for all $x$ in the unit interval. We propose honest calibration assessment based on novel confidence bands for the calibration curve, which are valid subject to only the natural assumption of isotonicity. Besides testing the classical goodness-of-fit null hypothesis of perfect calibration, our bands facilitate inverted goodness-of-fit tests whose rejection allows for the sought-after conclusion of a sufficiently well-specified model. We show that our bands have a finite-sample coverage guarantee, are narrower than those of existing approaches, and adapt to the local smoothness of the calibration curve $p$ and the local variance of the binary observations. In an application to modelling predictions of an infant having low birth weight, the bounds give informative insights into model calibration. |
doi_str_mv | 10.1093/biomet/asac068 |
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Probability predictions from binary regressions or machine learning methods ought to be calibrated: if an event is predicted to occur with probability $x$, it should materialize with approximately that frequency, which means that the so-called calibration curve $p(\cdot)$ should equal the identity, i.e., $p(x) = x$ for all $x$ in the unit interval. We propose honest calibration assessment based on novel confidence bands for the calibration curve, which are valid subject to only the natural assumption of isotonicity. Besides testing the classical goodness-of-fit null hypothesis of perfect calibration, our bands facilitate inverted goodness-of-fit tests whose rejection allows for the sought-after conclusion of a sufficiently well-specified model. We show that our bands have a finite-sample coverage guarantee, are narrower than those of existing approaches, and adapt to the local smoothness of the calibration curve $p$ and the local variance of the binary observations. In an application to modelling predictions of an infant having low birth weight, the bounds give informative insights into model calibration.</description><identifier>ISSN: 0006-3444</identifier><identifier>EISSN: 1464-3510</identifier><identifier>DOI: 10.1093/biomet/asac068</identifier><language>eng</language><publisher>Oxford: Oxford University Press</publisher><subject>Birth weight ; Calibration ; Goodness of fit ; Isotonicity ; Low birth weight ; Machine learning ; Predictions ; Smoothness ; Statistical tests</subject><ispartof>Biometrika, 2023-09, Vol.110 (3), p.663-680</ispartof><rights>The Author(s) 2022. Published by Oxford University Press on behalf of the Biometrika Trust. All rights reserved. For permissions, please email: journals.permissions@oup.com 2022</rights><rights>The Author(s) 2022. Published by Oxford University Press on behalf of the Biometrika Trust. All rights reserved. For permissions, please email: journals.permissions@oup.com</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c341t-3a36a5a4eb8d48e8d991397bc5a51d9ae2b7b616b60ae22fb2a96d8f7224ee373</citedby><cites>FETCH-LOGICAL-c341t-3a36a5a4eb8d48e8d991397bc5a51d9ae2b7b616b60ae22fb2a96d8f7224ee373</cites><orcidid>0000-0002-8322-360X ; 0000-0002-5916-9746</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,1578,27901,27902</link.rule.ids></links><search><creatorcontrib>Dimitriadis, Timo</creatorcontrib><creatorcontrib>Dümbgen, Lutz</creatorcontrib><creatorcontrib>Henzi, Alexander</creatorcontrib><creatorcontrib>Puke, Marius</creatorcontrib><creatorcontrib>Ziegel, Johanna</creatorcontrib><title>Honest calibration assessment for binary outcome predictions</title><title>Biometrika</title><description>Summary
Probability predictions from binary regressions or machine learning methods ought to be calibrated: if an event is predicted to occur with probability $x$, it should materialize with approximately that frequency, which means that the so-called calibration curve $p(\cdot)$ should equal the identity, i.e., $p(x) = x$ for all $x$ in the unit interval. We propose honest calibration assessment based on novel confidence bands for the calibration curve, which are valid subject to only the natural assumption of isotonicity. Besides testing the classical goodness-of-fit null hypothesis of perfect calibration, our bands facilitate inverted goodness-of-fit tests whose rejection allows for the sought-after conclusion of a sufficiently well-specified model. We show that our bands have a finite-sample coverage guarantee, are narrower than those of existing approaches, and adapt to the local smoothness of the calibration curve $p$ and the local variance of the binary observations. In an application to modelling predictions of an infant having low birth weight, the bounds give informative insights into model calibration.</description><subject>Birth weight</subject><subject>Calibration</subject><subject>Goodness of fit</subject><subject>Isotonicity</subject><subject>Low birth weight</subject><subject>Machine learning</subject><subject>Predictions</subject><subject>Smoothness</subject><subject>Statistical tests</subject><issn>0006-3444</issn><issn>1464-3510</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNqFkEFLxDAQhYMoWFevngOePHQ3adI0BS-yuK6w4EXPYZKmkGXb1CQ9-O_N0r17mhn43pvHQ-iRkjUlLdto5webNhDBECGvUEG54CWrKblGBSFElIxzfovuYjyeT1GLAr3s_WhjwgZOTgdIzo8YYrQxDnZMuPcBazdC-MV-TiY_wFOwnTNnMN6jmx5O0T5c5gp9796-tvvy8Pn-sX09lIZxmkoGTEAN3GrZcWll17aUtY02NdS0a8FWutGCCi1I3qteV9CKTvZNVXFrWcNW6GnxnYL_mXNcdfRzGPNLxQjPZlRSlqn1QpngYwy2V1NwQ46uKFHnhtTSkLo0lAXPi8DP03_sH-qdap0</recordid><startdate>20230901</startdate><enddate>20230901</enddate><creator>Dimitriadis, Timo</creator><creator>Dümbgen, Lutz</creator><creator>Henzi, Alexander</creator><creator>Puke, Marius</creator><creator>Ziegel, Johanna</creator><general>Oxford University Press</general><general>Oxford Publishing Limited (England)</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7QO</scope><scope>8FD</scope><scope>FR3</scope><scope>P64</scope><orcidid>https://orcid.org/0000-0002-8322-360X</orcidid><orcidid>https://orcid.org/0000-0002-5916-9746</orcidid></search><sort><creationdate>20230901</creationdate><title>Honest calibration assessment for binary outcome predictions</title><author>Dimitriadis, Timo ; Dümbgen, Lutz ; Henzi, Alexander ; Puke, Marius ; Ziegel, Johanna</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c341t-3a36a5a4eb8d48e8d991397bc5a51d9ae2b7b616b60ae22fb2a96d8f7224ee373</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Birth weight</topic><topic>Calibration</topic><topic>Goodness of fit</topic><topic>Isotonicity</topic><topic>Low birth weight</topic><topic>Machine learning</topic><topic>Predictions</topic><topic>Smoothness</topic><topic>Statistical tests</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dimitriadis, Timo</creatorcontrib><creatorcontrib>Dümbgen, Lutz</creatorcontrib><creatorcontrib>Henzi, Alexander</creatorcontrib><creatorcontrib>Puke, Marius</creatorcontrib><creatorcontrib>Ziegel, Johanna</creatorcontrib><collection>CrossRef</collection><collection>Biotechnology Research Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Biotechnology and BioEngineering Abstracts</collection><jtitle>Biometrika</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dimitriadis, Timo</au><au>Dümbgen, Lutz</au><au>Henzi, Alexander</au><au>Puke, Marius</au><au>Ziegel, Johanna</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Honest calibration assessment for binary outcome predictions</atitle><jtitle>Biometrika</jtitle><date>2023-09-01</date><risdate>2023</risdate><volume>110</volume><issue>3</issue><spage>663</spage><epage>680</epage><pages>663-680</pages><issn>0006-3444</issn><eissn>1464-3510</eissn><abstract>Summary
Probability predictions from binary regressions or machine learning methods ought to be calibrated: if an event is predicted to occur with probability $x$, it should materialize with approximately that frequency, which means that the so-called calibration curve $p(\cdot)$ should equal the identity, i.e., $p(x) = x$ for all $x$ in the unit interval. We propose honest calibration assessment based on novel confidence bands for the calibration curve, which are valid subject to only the natural assumption of isotonicity. Besides testing the classical goodness-of-fit null hypothesis of perfect calibration, our bands facilitate inverted goodness-of-fit tests whose rejection allows for the sought-after conclusion of a sufficiently well-specified model. We show that our bands have a finite-sample coverage guarantee, are narrower than those of existing approaches, and adapt to the local smoothness of the calibration curve $p$ and the local variance of the binary observations. In an application to modelling predictions of an infant having low birth weight, the bounds give informative insights into model calibration.</abstract><cop>Oxford</cop><pub>Oxford University Press</pub><doi>10.1093/biomet/asac068</doi><tpages>18</tpages><orcidid>https://orcid.org/0000-0002-8322-360X</orcidid><orcidid>https://orcid.org/0000-0002-5916-9746</orcidid><oa>free_for_read</oa></addata></record> |
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source | Oxford University Press Journals All Titles (1996-Current) |
subjects | Birth weight Calibration Goodness of fit Isotonicity Low birth weight Machine learning Predictions Smoothness Statistical tests |
title | Honest calibration assessment for binary outcome predictions |
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