condensité

(pronounciation: kon-dahn-see-tay, like the French word for "density")

Installation.

pip install condensite

Paper. Transforming Conditional Density Estimation Into a Single Nonparametric Regression Task

Summary. The approach behind condensité enables transforming conditional density estimation into a single nonparametric regression task. This package provides an implementation that allows turning regressors from popular machine learning libraries such as sklearn or torch into conditional density estimators. See below for a complete example, further ones can be found in src/examples.

Benchmarking. For a benchmarking effort of conditional density estimators, see https://scoringbench.com/, which includes condensité using lightGBM as a regressor. Note that condensité is a general approach that could be used in combination with any regressor.

Example.

import torch
import numpy as np
import condensite as cde
from sklearn.ensemble import HistGradientBoostingRegressor

# create a condensité predictor based on sklearn's HistGradientBoostingRegressor
class TreePredictor(cde.CondensitePredictor):
    def __init__(self, params):
        self.tree = HistGradientBoostingRegressor(**params)

    def device(self):
        return "cpu"

    def to(self, device):
        return self

    def forward(self, x):
        return self.tree.predict(x)

    def predict(self, x):
        return torch.tensor(self.forward(x), dtype=torch.float32)

    def fit(self, dataset: cde.RepeatDataset):
        # create data loader (c.f. cde.RepeatDataset and cde.concat_collate)
        train_DL = torch.utils.data.DataLoader(dataset=dataset,                 
                                               batch_size=dataset.n*dataset.M, 
                                               shuffle=True, 
                                               collate_fn=cde.concat_collate)
        xtorch, ytorch = next(iter(train_DL))  # single batch of all data
        x, y = xtorch.numpy(), ytorch.numpy()
        self.tree.fit(x, y)
        return np.mean(np.square(self.tree.predict(x)-y))  # mse

# instantiate and wrap using Condensite
tree_predictor = TreePredictor(params={
    'max_bins': 40,
    'max_leaf_nodes': 100,
    'l2_regularization': 0.1,
})
hgb_model = cde.Condensite(tree_predictor, h=0.01, M=100, name='hgb_model')

# generate some data and fit
def sample_data(n_obs=1000, n_features=10):
    x = torch.empty((n_obs, n_features)).normal_(0,1)
    x1 = x[:, 0]
    std = torch.sqrt(0.25 + x1**2)
    noise = torch.distributions.Normal(torch.zeros_like(x1), std).sample()
    y = x1 + noise
    return x, y

# fit conditional density estimator
x_train, y_train = sample_data()
hgb_model.fit(x_train, y_train, train_frac=0.8, n_grid_ISE=100)

# evaluate fit out-of-sample
x_test, y_test = sample_data()
test_ISE = cde.utils.ISE(hgb_model, x_test, y_test, n_grid=100).item()
print(f'{hgb_model.name}:\t {test_ISE=:.4f}')

Reference. If you find our algorithms useful please consider citing

@misc{reisach2025condensite,
    title={Transforming Conditional Density Estimation Into a Single Nonparametric Regression Task}, 
    author={Alexander G. Reisach and Olivier Collier and Alex Luedtke and Antoine Chambaz},
    year={2025},
    url={https://arxiv.org/abs/2511.18530}, 
}