# Partition Tree: Conditional Density Estimation over General Outcome Spaces

arXiv: https://arxiv.org/abs/2602.04042 · HTML: https://mlsanity.com/paper/2602.04042/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 33 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 3 of 3)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Probabilistic supervised learning](https://mlsanity.com/paper/1801.00753/) (2018)
- [Conditional Density Estimation with Histogram Trees](https://mlsanity.com/paper/2410.11449/) (2024)

## Abstract (arXiv)

We propose Partition Tree, a novel tree-based framework for conditional density estimation over general outcome spaces that supports both continuous and categorical variables within a unified formulation. Our approach models conditional distributions as piecewise-constant densities on data-adaptive partitions and learns trees by directly minimizing conditional negative log-likelihood. This yields a scalable, nonparametric alternative to existing probabilistic trees that does not make parametric assumptions about the target distribution. We further introduce Partition Forest, a bagging extension obtained by averaging conditional densities. Empirically, we demonstrate improved probabilistic prediction over CART-style trees and competitive performance compared to state-of-the-art probabilistic tree methods and Random Forests.