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Describe the bug
In MapieRegressor, the quantile calculation does not allow us to check the coverage validity when the number of calibration data is very small.
Describe the bug
In
MapieRegressor
, the quantile calculation does not allow us to check the coverage validity when the number of calibration data is very small.To Reproduce
A rigorous approach to testing the validity of the coverage was carried out by Mahdi Torabi Rad (see his notebook: https://github.com/mtorabirad/MLBoost/blob/main/Episode15/Episode15Main.ipynb) in the special case where the number of calibration data is very small (6 in the following illustration).
Expected behavior$|(n+1)(1−α)|/n$ ) to check the validity of the coverage for any number of calibration data.
Use the corrected quantile (
Screenshots
![image](https://private-user-images.githubusercontent.com/124613154/333895351-ad038267-da75-46a7-8967-f37b115195e1.png?jwt=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJnaXRodWIuY29tIiwiYXVkIjoicmF3LmdpdGh1YnVzZXJjb250ZW50LmNvbSIsImtleSI6ImtleTUiLCJleHAiOjE3Mzg5MjQ5ODksIm5iZiI6MTczODkyNDY4OSwicGF0aCI6Ii8xMjQ2MTMxNTQvMzMzODk1MzUxLWFkMDM4MjY3LWRhNzUtNDZhNy04OTY3LWYzN2IxMTUxOTVlMS5wbmc_WC1BbXotQWxnb3JpdGhtPUFXUzQtSE1BQy1TSEEyNTYmWC1BbXotQ3JlZGVudGlhbD1BS0lBVkNPRFlMU0E1M1BRSzRaQSUyRjIwMjUwMjA3JTJGdXMtZWFzdC0xJTJGczMlMkZhd3M0X3JlcXVlc3QmWC1BbXotRGF0ZT0yMDI1MDIwN1QxMDM4MDlaJlgtQW16LUV4cGlyZXM9MzAwJlgtQW16LVNpZ25hdHVyZT1lYTBkNDBlYTM4MDBhNjNhYTdhODNmNjMyZDVlNTcwNTE5ZTJlMjVmZjMwNzE3MzZhMGYzN2RlZGM5NTczYThiJlgtQW16LVNpZ25lZEhlYWRlcnM9aG9zdCJ9.-sgOsvNFyMOgWKxMUDGbOwc0NwzzEhsKj5Zuch4ylUQ)
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