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Package implementing various parametric and nonparametric methods for conditional density estimation


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Conditional Density Estimation (CDE)


Implementations of various methods for conditional density estimation

  • Parametric neural network based methods
    • Mixture Density Network (MDN)
    • Kernel Mixture Network (KMN)
    • Normalizing Flows (NF)
  • Nonparametric methods
    • Conditional Kernel Density Estimation (CKDE)
    • Neighborhood Kernel Density Estimation (NKDE)
  • Semiparametric methods
    • Least Squares Conditional Density Estimation (LSKDE)

Beyond estimating conditional probability densities, the package features extensive functionality for computing:

  • Centered moments: mean, covariance, skewness and kurtosis
  • Statistical divergences: KL-divergence, JS-divergence, Hellinger distance
  • Percentiles and expected shortfall

For the parametric models (MDN, KMN, NF), we recommend the usage of noise regularization which is supported by our implementation. For details, we refer to the paper Noise Regularization for Conditional Density Estimation.


To use the library, you can directly use the python package index:

pip install cde

or clone the GitHub repository and run

pip install .

Note that the package only supports tensorflow versions between 1.4 and 1.7.

Documentation and paper

See the documentation here. A paper on best practices and benchmarks on conditional density estimation with neural networks that makes extensive use of this library can be found here.


The following code snipped holds an easy example that demonstrates how to use the cde package.

from cde.density_simulation import SkewNormal
from cde.density_estimator import KernelMixtureNetwork
import numpy as np

""" simulate some data """
density_simulator = SkewNormal(random_seed=22)
X, Y = density_simulator.simulate(n_samples=3000)

""" fit density model """
model = KernelMixtureNetwork("KDE_demo", ndim_x=1, ndim_y=1, n_centers=50,
                             x_noise_std=0.2, y_noise_std=0.1, random_seed=22), Y)

""" query the conditional pdf and cdf """
x_cond = np.zeros((1, 1))
y_query = np.ones((1, 1)) * 0.1
prob = model.pdf(x_cond, y_query)
cum_prob = model.cdf(x_cond, y_query)

""" compute conditional moments & VaR  """
mean = model.mean_(x_cond)[0][0]
std = model.std_(x_cond)[0][0]
skewness = model.skewness(x_cond)[0]


If you use our CDE implementation in your research, you can cite it as follows:

  title={Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks},
  author={Rothfuss, Jonas and Ferreira, Fabio and Walther, Simon and Ulrich, Maxim},

If you use noise regularization for regularizing the MDN, KMN or NF conditional density model, please cite

    title={Noise Regularization for Conditional Density Estimation},
    author={Jonas Rothfuss and Fabio Ferreira and Simon Boehm and Simon Walther 
            and Maxim Ulrich and Tamim Asfour and Andreas Krause},


  • creating a branch just for our conditional estimators + python package
  • support for TensorFlow versions > 1.7 (your help would be highly appreciated here)


Package implementing various parametric and nonparametric methods for conditional density estimation







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