# Random Forests for Adaptive Nearest Neighbor Estimation of Information-Theoretic Quantities

arXiv: https://arxiv.org/abs/1907.00325 · HTML: https://mlsanity.com/paper/1907.00325/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2019.

## Built on by (most cited first, 2 of 2)

- [h-calibration: Rethinking Classifier Recalibration with Probabilistic Error-Bounded Objective](https://mlsanity.com/paper/2506.17968/) (2025)
- [Non-Stationarity Breaks Permutation Surrogates in Multi-Agent Reinforcement Learning: Diagnosis and Remedies](https://mlsanity.com/paper/2604.23716/) (2026)

## Abstract (arXiv)

Information-theoretic quantities, such as conditional entropy and mutual information, are critical data summaries for quantifying uncertainty. Current widely used approaches for computing such quantities rely on nearest neighbor methods and exhibit both strong performance and theoretical guarantees in certain simple scenarios. However, existing approaches fail in high-dimensional settings and when different features are measured on different scales.We propose decision forest-based adaptive nearest neighbor estimators and show that they are able to effectively estimate posterior probabilities, conditional entropies, and mutual information even in the aforementioned settings.We provide an extensive study of efficacy for classification and posterior probability estimation, and prove certain forest-based approaches to be consistent estimators of the true posteriors and derived information-theoretic quantities under certain assumptions. In a real-world connectome application, we quantify the uncertainty about neuron type given various cellular features in the Drosophila larva mushroom body, a key challenge for modern neuroscience.