Property Elicitation on Imprecise Probabilities

TL;DR

This paper extends property elicitation to imprecise probabilities, providing conditions for what can be learned in distributionally robust settings and connecting it to classical properties via maximum Bayes risk.

Contribution

It introduces necessary and sufficient conditions for the elicitability of IP-properties, generalizing property elicitation to imprecise probabilities in robust frameworks.

Findings

Necessary and sufficient conditions for IP-property elicitability.

Connection between IP-properties and classical properties via maximum Bayes risk.

Framework applicable to distributionally robust optimization and multi-distribution learning.

Abstract

Property elicitation studies which attributes of a probability distribution can be determined by minimizing a risk. We investigate a generalization of property elicitation to imprecise probabilities (IP). This investigation is motivated by distributionally robust optimization and multi-distribution learning. Both those frameworks replace the minimization of a single risk over a (precise) probability by a maximin risk minimization over a set of probabilities -- i.e. an IP. We show what can be learned in those multi-distribution setups by providing necessary and sufficient conditions for the elicitability of an IP-property. Central to these conditions is the observation made in related literature that the elicited IP-property is the corresponding classical property of the probability in the IP with the maximum Bayes risk.