Treeffuser: Probabilistic Predictions via Conditional Diffusions with Gradient-Boosted Trees

TL;DR

Treeffuser introduces a flexible, non-parametric probabilistic prediction method for tabular data using conditional diffusion models estimated with gradient-boosted trees, outperforming existing approaches in calibration and versatility.

Contribution

It presents a novel non-parametric probabilistic prediction framework combining diffusion models with gradient-boosted trees for tabular data.

Findings

Outperforms existing probabilistic methods in calibration.

Handles multivariate, multimodal, and skewed responses effectively.

Demonstrates versatility with real-world inventory allocation data.

Abstract

Probabilistic prediction aims to compute predictive distributions rather than single point predictions. These distributions enable practitioners to quantify uncertainty, compute risk, and detect outliers. However, most probabilistic methods assume parametric responses, such as Gaussian or Poisson distributions. When these assumptions fail, such models lead to bad predictions and poorly calibrated uncertainty. In this paper, we propose Treeffuser, an easy-to-use method for probabilistic prediction on tabular data. The idea is to learn a conditional diffusion model where the score function is estimated using gradient-boosted trees. The conditional diffusion model makes Treeffuser flexible and non-parametric, while the gradient-boosted trees make it robust and easy to train on CPUs. Treeffuser learns well-calibrated predictive distributions and can handle a wide range of regression tasks -- including those with multivariate, multimodal, and skewed responses. We study Treeffuser on synthetic and real data and show that it outperforms existing methods, providing better calibrated probabilistic predictions. We further demonstrate its versatility with an application to inventory allocation under uncertainty using sales data from Walmart. We implement Treeffuser in https://github.com/blei-lab/treeffuser.