# Conditional Density Estimation (CDE)

## Description

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.

## Installation

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.

## Usage

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)
model.fit(X, 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]``````

## Citing

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

``````@article{rothfuss2019conditional,
title={Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks},
author={Rothfuss, Jonas and Ferreira, Fabio and Walther, Simon and Ulrich, Maxim},
journal={arXiv:1903.00954},
year={2019}
}
``````

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

``````@article{rothfuss2019noisereg,
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},
year={2019},
journal={arXiv:1907.08982},
}``````

## Todo

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