# Generative modeling of density regression through tree flows

arXiv: https://arxiv.org/abs/2406.05260 · HTML: https://mlsanity.com/paper/2406.05260/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 17 references that are in the map.
- First posted on arXiv 7 Jun 2024.

## Builds on (most cited first, 11 of 11)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Why do tree-based models still outperform deep learning on tabular data?](https://mlsanity.com/paper/2207.08815/) (2022)
- [NGBoost: Natural Gradient Boosting for Probabilistic Prediction](https://mlsanity.com/paper/1910.03225/) (2019)
- [Conditional Density Estimation with Bayesian Normalising Flows](https://mlsanity.com/paper/1802.04908/) (2018)
- [Learning and Policy Search in Stochastic Dynamical Systems with Bayesian Neural Networks](https://mlsanity.com/paper/1605.07127/) (2016)
- [Deep Gaussian Processes for Regression using Approximate Expectation Propagation](https://mlsanity.com/paper/1602.04133/) (2016)
- [Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks](https://mlsanity.com/paper/1903.00954/) (2019)
- [Probabilistic Gradient Boosting Machines for Large-Scale Probabilistic Regression](https://mlsanity.com/paper/2106.01682/) (2021)
- [Unsupervised tree boosting for learning probability distributions](https://mlsanity.com/paper/2101.11083/) (2021)
- [Deconvolutional Density Network: Modeling Free-Form Conditional Distributions](https://mlsanity.com/paper/2105.14367/) (2021)
- [RoNGBa: A Robustly Optimized Natural Gradient Boosting Training Approach with Leaf Number Clipping](https://mlsanity.com/paper/1912.02338/) (2019)

## Abstract (arXiv)

A common objective in the analysis of tabular data is estimating the conditional distribution (in contrast to only producing predictions) of a set of "outcome" variables given a set of "covariates", which is sometimes referred to as the "density regression" problem. Beyond estimation on the conditional distribution, the generative ability of drawing synthetic samples from the learned conditional distribution is also desired as it further widens the range of applications. We propose a flow-based generative model tailored for the density regression task on tabular data. Our flow applies a sequence of tree-based piecewise-linear transforms on initial uniform noise to eventually generate samples from complex conditional densities of (univariate or multivariate) outcomes given the covariates and allows efficient analytical evaluation of the fitted conditional density on any point in the sample space. We introduce a training algorithm for fitting the tree-based transforms using a divide-and-conquer strategy that transforms maximum likelihood training of the tree-flow into training a collection of binary classifiers--one at each tree split--under cross-entropy loss. We assess the performance of our method under out-of-sample likelihood evaluation and compare it with a variety of state-of-the-art conditional density learners on a range of simulated and real benchmark tabular datasets. Our method consistently achieves comparable or superior performance at a fraction of the training and sampling budget. Finally, we demonstrate the utility of our method's generative ability through an application to generating synthetic longitudinal microbiome compositional data based on training our flow on a publicly available microbiome study.