Mode Estimation with Partial Feedback
Charles Arnal, Vivien Cabannes, Vianney Perchet
TL;DR
This work tackles mode estimation under partial feedback, formulating a minimal-query framework that blends weak supervision with active information gathering. It develops an empirical mode estimator and proves tight information-theoretic bounds, then introduces a spectrum of coding- and search-based algorithms that progressively exploit entropy coding and coarse statistics. The culminating Set Elimination algorithm unifies truncated search and bandit-inspired elimination to achieve near-optimal query complexity, with practical implications for scalable weakly supervised online learning. A public codebase accompanies the results, enabling practitioners to apply these strategies to real-world partial-feedback problems.
Abstract
The combination of lightly supervised pre-training and online fine-tuning has played a key role in recent AI developments. These new learning pipelines call for new theoretical frameworks. In this paper, we formalize core aspects of weakly supervised and active learning with a simple problem: the estimation of the mode of a distribution using partial feedback. We show how entropy coding allows for optimal information acquisition from partial feedback, develop coarse sufficient statistics for mode identification, and adapt bandit algorithms to our new setting. Finally, we combine those contributions into a statistically and computationally efficient solution to our problem.