Active Nearest Neighbor Regression Through Delaunay Refinement

TL;DR

This paper presents ANNR, an active nearest neighbor regression algorithm that uses Delaunay refinement to improve function approximation, outperforming existing methods like DEFER in various applications.

Contribution

The paper introduces ANNR, a novel active regression method leveraging Delaunay refinement, with theoretical guarantees and superior empirical performance over DEFER.

Findings

ANNR outperforms DEFER on benchmark functions.

ANNR effectively handles real-world problems like gravitational wave inference.

The method provides theoretical halting guarantees.

Abstract

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.