Primary Submission Category: Heterogeneous Treatment Effects
Fisher–Rao Gradient Flows for Semiparametric Estimation of Parameters Lacking a Canonical Gradient
Authors: Kaiwen HOU, Mark van der Laan,
Presenting Author: Kaiwen HOU*
We introduce a unified framework that bridges geometric gradient flow methods with semiparametric efficiency theory, specifically addressing parameters that lack a conventional canonical gradient. By generalizing the Jordan–Kinderlehrer–Otto scheme under the Hellinger distance, we equip the space of probability distributions with a Fisher–Rao geometry and construct a natural gradient flow for likelihood maximization. This approach characterizes the universal least favorable path in one-step TMLE as a Fisher–Rao gradient trajectory, thereby connecting the geometric steepest descent to classical one‐step estimation. We establish well-posedness of the underlying infinite-dimensional PDE and demonstrate that the resulting one-step estimators attain asymptotic efficiency in both parametric and functional models. These results provide robust tools for efficient inference in semiparametric settings where standard efficiency theory does not apply.