Property Elicitation on Imprecise Probabilities
This work addresses a theoretical gap in machine learning for handling uncertainty in multi-distribution settings, but it appears incremental as it extends existing elicitation concepts.
The paper tackles the problem of generalizing property elicitation to imprecise probabilities, motivated by multi-distribution learning, and provides necessary conditions for elicitability and an explanation through Bayes pairs.
Property elicitation studies which attributes of a probability distribution can be determined by minimising a risk. We investigate a generalisation of property elicitation to imprecise probabilities (IP). This investigation is motivated by multi-distribution learning, which takes the classical machine learning paradigm of minimising a single risk over a (precise) probability and replaces it with $Γ$-maximin risk minimization over an IP. We provide necessary conditions for elicitability of a IP-property. Furthermore, we explain what an elicitable IP-property actually elicits through Bayes pairs -- the elicited IP-property is the corresponding standard property of the maximum Bayes risk distribution.