B0500
Title: Fundamental limits of structure-agnostic functional estimation
Authors: Edward Kennedy - Carnegie Mellon University (United States) [presenting]
Abstract: The fundamental limits of structure-agnostic functional estimation are investigated, where relatively weak conditions are placed on the underlying nuisance functions. It is shown that there is a strong sense in which existing first-order methods are optimal. Particularly, it is shown that for several canonical integral functionals of interest, it is impossible to improve on first-order estimators without making further, strong structural assumptions. This goal is achieved by providing a formalization of the problem of functional estimation with black-box nuisance function estimates and deriving minimax lower bounds for this problem. Results highlight some clear tradeoffs in functional estimation if the wish is to remain agnostic to the underlying nuisance function spaces, impose only high-level rate conditions, and maintain compatibility with black-box nuisance estimators then first-order methods are optimal. When a better understanding of the structure of the underlying nuisance functions is obtained, then carefully constructed higher-order estimators can outperform first-order estimators.
