Active Nearest Neighbor Regression Through Delaunay Refinement
This work addresses active learning for function approximation, offering improvements over existing methods, though it appears incremental as it builds on prior approaches like DEFER.
The paper tackles the problem of active function approximation by introducing the Active Nearest Neighbor Regressor (ANNR), which uses Voronoi-Delaunay geometry to select query points and subdivide space, outperforming the DEFER baseline in experiments on closed-form functions and real-world tasks like gravitational wave inference.
We introduce an algorithm for active function approximation based on nearest neighbor regression. Our Active Nearest Neighbor Regressor (ANNR) relies on the Voronoi-Delaunay framework from computational geometry to subdivide the space into cells with constant estimated function value and select novel query points in a way that takes the geometry of the function graph into account. We consider the recent state-of-the-art active function approximator called DEFER, which is based on incremental rectangular partitioning of the space, as the main baseline. The ANNR addresses a number of limitations that arise from the space subdivision strategy used in DEFER. We provide a computationally efficient implementation of our method, as well as theoretical halting guarantees. Empirical results show that ANNR outperforms the baseline for both closed-form functions and real-world examples, such as gravitational wave parameter inference and exploration of the latent space of a generative model.