drforest

drforest is a Python and Rust implementation of distributional random forests. A fitted forest estimates a conditional distribution as sparse weights over the training responses, then derives means, quantiles, CDFs, and distributional scores from the same estimate.

The package supports scalar and multivariate responses. Split search is Rust-backed and offers CART, Gaussian maximum mean discrepancy (MMD), adaptive and anisotropic MMD variants, and sliced Wasserstein separation.

Installation

Install the published package from PyPI:

python -m pip install drforest

Python 3.11 through 3.14 are supported. Binary wheels are published for Linux, macOS, and Windows on supported architectures; pip falls back to the source distribution when no compatible wheel is available.

Quick start

The estimator accepts ordinary one-dimensional regression targets. By default, it uses distribution-sensitive MMD splitting.

import numpy as np

from drforest import DistributionalRandomForest

rng = np.random.default_rng(0)
X = rng.normal(size=(500, 4))
y = X[:, 0] + (0.5 + np.abs(X[:, 1])) * rng.normal(size=500)

X_train, X_test = X[:400], X[400:]
y_train, y_test = y[:400], y[400:]

forest = DistributionalRandomForest(
    criterion="mmd",
    n_estimators=20,
    subsample=0.5,
    min_samples_leaf=5,
    honesty_fraction=0.5,
    colsample=0.7,
    max_cutpoints=32,
    random_state=0,
).fit(X_train, y_train)

mean = forest.predict(X_test)
quantiles = forest.predict_quantiles(X_test, [0.1, 0.5, 0.9])
cdf = forest.predict_cdf(X_test, [-1.0, 0.0, 1.0])

assert mean.shape == (100,)
assert quantiles.shape == (100, 3)
assert cdf.shape == (100, 3)

For a two-dimensional response array with shape (n_samples, n_outputs), predict returns (n_test, n_outputs). Quantile and CDF predictions return (n_test, n_outputs, n_values).

Prediction interface

• predict(X) returns the conditional mean.
• predict_quantiles(X, quantiles) returns marginal conditional quantiles.
• predict_cdf(X, thresholds) evaluates marginal conditional CDFs.
• predict_weights(X) returns the sparse conditional weight matrix.

The prediction methods retain the training responses during fit; callers do not need to pass them again.

Split criteria

Pass a built-in name through criterion:

Name	Split geometry	Built-in configuration
"mmd" or "mmd_rff"	Gaussian MMD	128 random Fourier features, median bandwidth
"cart"	Multivariate mean separation	No additional configuration
"anisotropic_mmd"	Coordinatewise-bandwidth MMD	128 random Fourier features
"adaptive_mmd"	Adaptive-frequency MMD	128 pooled, 32 selected features
"sliced_wasserstein"	Sliced Wasserstein distance	128 projections

If neither criterion nor criterion_factory is supplied, "mmd" is used. An explicit criterion name takes precedence when both are supplied.

Research and custom targets

The sparse weight matrix remains the core representation for custom targets, metrics, shrinkage, and criterion experiments:

from drforest.metrics import mean_crps
from drforest.targets import weighted_mean, weighted_quantile

weights = forest.predict_weights(X_test)
mean = weighted_mean(weights, forest.y_train_)
quantiles = weighted_quantile(weights, forest.y_train_, [0.1, 0.5, 0.9])
score = mean_crps(weights, forest.y_train_, y_test[:, None])

For a custom or specially configured split criterion, provide a factory that receives the validated two-dimensional training responses once:

from drforest import DistributionalRandomForest
from drforest.criteria import MmdRffCriterion
from drforest.features.rff import fixed_bandwidth

forest = DistributionalRandomForest(
    criterion_factory=lambda y: MmdRffCriterion.from_data(
        y,
        n_features=512,
        bandwidth_rule=fixed_bandwidth(1.0),
    ),
    n_estimators=5,
    max_cutpoints=32,
    random_state=0,
).fit(X_train, y_train)

Statistical scope

Version 0.2.0 is a research release. The core implementation is tested, but the public API may still change. The current fixed-fraction subsampling interface is intended for prediction and benchmarking; it does not claim the inference-valid regime required by the asymptotic forest theory. Missing-value handling is not implemented.

The accompanying characterization note is available as a repository PDF. It studies when distributional splitting helps, compares the implemented criteria, and gives a finite-node analysis of mean versus kernel-mean split signal. An arXiv link and formal citation will be added after the note is posted.

Design

forest structure -> sparse conditional weights -> targets and scores

This keeps split geometry separate from downstream estimation. A criterion can change without changing mean, quantile, CDF, or scoring implementations, and the same fitted forest can serve multiple targets.

Trees support honest structure/leaf sample splitting, explicit per-tree and per-node random-number streams, row subsampling, feature subsampling, and a shared candidate-cutpoint cap. MMD bandwidths are configured once from the full training response; random Fourier frequencies are resampled per node.

Benchmarks and paper

Study entry points live in benchmarks/studies:

pixi run python benchmarks/studies/run_synthetic_splitting.py
pixi run python benchmarks/studies/run_real_benchmark.py \
  --datasets diabetes \
  --criteria cart mmd_rff \
  --honesty-fractions 0.5 0.0

Generated datasets and result files are intentionally not tracked. Tables, figures, LaTeX sources, and the compiled note are committed under paper.

Development

Install the development environment and pre-commit hooks with:

git clone https://github.com/silaskoemen/drforest.git
cd drforest
pixi install
pixi run build-rust
pixi run setup

Before submitting a change, run:

pixi run lint
pixi run pytest
pixi run build-wheel
pixi run check-wheel

Security issues should be reported through SECURITY.md.

Citation

A citation for the characterization note will be added after its arXiv release. Until then, cite the repository and the specific release used so the code and results remain reproducible.

License

drforest is released under the MIT License.