Smooth densities and generative modeling with unsupervised random forests

Density estimation is a fundamental problem in statistics, and any attempt to do so in high dimensions typically requires strong assumptions or complex deep learning architectures. An important application for density estimators is synthetic data generation, an area currently dominated by neural networks that often demand enormous training datasets and extensive tuning. We propose a new method based on unsupervised random forests for estimating smooth densities in arbitrary dimensions without parametric constraints, as well as generating realistic synthetic data. We prove the consistency of our approach and demonstrate its advantages over existing tree-based density estimators, which generally rely on ill-chosen split criteria and do not scale well with data dimensionality. Experiments illustrate that our algorithm compares favorably to state-of-the-art deep learning generative models, achieving superior performance in a range of benchmark trials while executing about two orders of magnitude faster on average. Our method is implemented in easy-to-use $\texttt{R}$ and Python packages.