An Uncertainty Principle for Simultaneous Statistical Learning and Error Assessment
A Cramer-Rao-style lower bound under squared loss showing that optimizing learning and reliably assessing the actual learning error from the same data are fundamentally at odds: the relative regret in learning is bounded below by the squared correlation between any unbiased error assessor and the true learning error. Framed as a Heisenberg-like uncertainty principle sharing the Cramer-Rao essence that constrained co-variation limits independent marginal variation, it implies reserving some information for error assessment rather than fully optimizing learning.
For a Special Issue of Statistics and Applications (http://www.ssca.org.in/journal) in Memory of C
This essay by Xiao-Li Meng argues for a Heisenberg-like uncertainty principle in statistical learning: using the same data both to optimize learning and to assess actual prediction error are fundamen…