Elicitation Complexity of Statistical Properties
Abstract
A property, or statistical functional, is said to be elicitable if it minimizes expected loss for some loss function. The study of which properties are elicitable sheds light on the capabilities and limitations of point estimation and empirical risk minimization. While recent work asks which properties are elicitable, we instead advocate for a more nuanced question: how many dimensions are required to indirectly elicit a given property? This number is called the elicitation complexity of the property. We lay the foundation for a general theory of elicitation complexity, including several basic results about how elicitation complexity behaves, and the complexity of standard properties of interest. Building on this foundation, our main result gives tight complexity bounds for the broad class of Bayes risks. We apply these results to several properties of interest, including variance, entropy, norms, and several classes of financial risk measures. We conclude with discussion and open directions.
Cite
@article{arxiv.1506.07212,
title = {Elicitation Complexity of Statistical Properties},
author = {Rafael Frongillo and Ian A. Kash},
journal= {arXiv preprint arXiv:1506.07212},
year = {2020}
}
Comments
This version fixes an error in the condition needed for the main lower bound and adds an application to Range Value at Risk, along with a substantial reorganization of the paper and numerous smaller changes. A previous version appeared in Neural Information Processing Systems 2015