# Active Nearest Neighbor Regression Through Delaunay Refinement

arXiv: https://arxiv.org/abs/2206.08061 · HTML: https://mlsanity.com/paper/2206.08061/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 48 references that are in the map.
- First posted on arXiv 16 Jun 2022.

## Builds on (most cited first, 12 of 12)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Generative Adversarial Active Learning](https://mlsanity.com/paper/1702.07956/) (2017)
- [Geometrically Enriched Latent Spaces](https://mlsanity.com/paper/2008.00565/) (2020)
- [Variational Bayesian Monte Carlo](https://mlsanity.com/paper/1810.05558/) (2018)
- [Efficient acquisition rules for model-based approximate Bayesian computation](https://mlsanity.com/paper/1704.00520/) (2017)
- [Dynamic nested sampling: an improved algorithm for parameter estimation and evidence calculation](https://mlsanity.com/paper/1704.03459/) (2017)
- [Active Nearest-Neighbor Learning in Metric Spaces](https://mlsanity.com/paper/1605.06792/) (2016)
- [Batch simulations and uncertainty quantification in Gaussian process surrogate approximate Bayesian computation](https://mlsanity.com/paper/1910.06121/) (2019)
- [Black-box density function estimation using recursive partitioning](https://mlsanity.com/paper/2010.13632/) (2020)

## Built on by (most cited first, 1 of 1)

- [Fitting scattered data with optional monotonicity constraints on GPU: LipFit package](https://mlsanity.com/paper/2606.04670/) (2026)

## Abstract (arXiv)

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.