This paper places conformal testing in a general framework of statistical hypothesis testing. A standard approach to testing a composite null hypothesis H is to test each of its elements and to reject H when each of its elements is rejected. It turns out that we can fully cover conformal testing using this approach only if we allow forgetting some of the data. However, we will see that the standard approach covers conformal testing in a weak asymptotic sense and under restrictive assumptions. I will also list several possible directions of further research, including developing a general scheme of online testing.
|Title of host publication||Conformal and Probabilistic Prediction and Applications|
|Subtitle of host publication||Proceedings of Machine Learning Research|
|Editors||Khuong Nguyen, Henrik Bostrom, Lars Carlsson|
|Number of pages||20|
|Publication status||Accepted/In press - May 2023|