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Roundtrip is a deep generative neural density estimator which exploits the advantage of GANs for generating samples and estimates density by either importance sampling or Laplace approximation. This repository provides source code and instructions for using Roundtrip on both simulation data and real data.

Table of Contents


  • TensorFlow==1.13.1
  • Python==2.7.1


Roundtrip can be downloaded by

git clone

Software has been tested on a Linux (Centos 7) and Python2.7 environment. A GPU card is recommended for accelerating the training process.


This section provides instructions on how to reproduce results in the original paper.

Simulation data

We tested Roundtrip on three types of simulation datasets. (1) Indepedent Gaussian mixture. (2) 8-octagon Gaussian mixture. (3) Involute.

The main python script is used for implementing Roundtrip. Model architecture for Roundtrip can be find in Data loader or data sampler can be find in

Taking the (1) for an example, one can run the following commond to train a Roundtrip model with indepedent Gaussian mixture data.

CUDA_VISIBLE_DEVICES=0 python  --dx 2 --dy 2 --train True --data indep_gmm --epochs 100 --cv_epoch 30 --patience 5
[dx]  --  dimension of latent space
[dy]  --  dimension of observation space
[train]  --  whethre use train mode
[data]  --  dataset name
[epochs] -- maximum training epoches
[cv_epoch] -- epoch where (cross) validation begins
[patience] -- patience for early stopping

After training the model, you will have three part of outputs, which are marked by a unique timestamp YYYYMMDD_HHMMSS. This timestamp records the exact time when you run the script.

  1. log files and estimated density can be found at folder data/density_est_YYYYMMDD_HHMMSS_indep_gmm_x_dim=2_y_dim=2_alpha=10.0_beta=10.0.

  2. Model weights will be saved at folder checkpoint/density_est_YYYYMMDD_HHMMSS_indep_gmm_x_dim=2_y_dim=2_alpha=10.0_beta=10.0.

  3. The training loss curves were recorded at folder graph/density_est_YYYYMMDD_HHMMSS_indep_gmm_x_dim=2_y_dim=2_alpha=10.0_beta=10.0, which can be visualized using TensorBoard.

Next, we want to visulize the estimated density on a 2D region. One can then run the following script.

CUDA_VISIBLE_DEVICES=0 python --data indep_gmm --epoch epoch --path path
[YYYYMMDD_HHMMSS] --  timestamp in the last training step
[epoch] -- epoch for loading model weights
[path] --path to data folder, e.g., `data/density_est_YYYYMMDD_HHMMSS_indep_gmm_x_dim=2_y_dim=2_alpha=10.0_beta=10.0`

we suggest to use the epoch recorded in the last line of the log_test.txt file in the output part 1). Then the estimated density (.png) on a 2D grid region will be saved in the same data folder data/density_est_YYYYMMDD_HHMMSS_indep_gmm_x_dim=2_y_dim=2_alpha=10.0_beta=10.0.

It also easy to implement Roundtrip with other two simulation datasets by changing the data.

  • 8-octagon Gaussian mixture Model training:
    CUDA_VISIBLE_DEVICES=0 python  --dx 2 --dy 2 --train True --data eight_octagon_gmm --epochs 300 --cv_epoch 200 --patience 5
    Density esitmation on a 2D grid region:
    CUDA_VISIBLE_DEVICES=0 python --data eight_octagon_gmm --epoch epoch --path path
  • involute Model training:
    CUDA_VISIBLE_DEVICES=0 python  --dx 2 --dy 2 --train True --data involute --epochs 300 --cv_epoch 200 --patience 5
    Density esitmation on a 2D grid region:
    CUDA_VISIBLE_DEVICES=0 python  --data involute --epoch epoch --path path

Real Data

Next, we tested Roundtrip on different types of real data including five datasets from UCI machine learning repository and two image datasets. We provided freely public access to all related datasets (UCI datasets, image datasets, and OODS datasets), which can be download from a zenodo repository. All you need is to download the corresponding dataset (e.g., AreM.tar.gz), uncompress the data under datasets folder. Please also note that we provided various of pretrain models for a quick implementation of Roundtrip without training (see pretrain models section).

UCI Datasets

The original UCI datasets were from UCI machine learning repository. As the real data has no groud truth for density, we evaluate Roundtrip by calculating the average log likelihood on the test data. Similar to the simulation data, we take AreM dataset for an example, one can directly run

CUDA_VISIBLE_DEVICES=0 python  --dx 3 --dy 6 --train True --data uci_AReM --epochs 300 --cv_epoch 20 --patience 10 --use_cv True

Note that all the dataset from UCI machine learning repository will be added a prefix uci_ to the data name. The average log likelihood and stantard deviation can be found in log_test.txt under data folder data/density_est_YYYYMMDD_HHMMSS_uci_AreM_x_dim=2_y_dim=2_alpha=10.0_beta=10.0.

We also provide scripts for implementing Roundtrip with other UCI dataset.

  • CASP
    CUDA_VISIBLE_DEVICES=0 python  --dx 5 --dy 9 --train True --data uci_CASP --epochs 300 --cv_epoch 20 --patience 10 --use_cv True
    CUDA_VISIBLE_DEVICES=0 python  --dx 8 --dy 21 --train True --data uci_HEPMASS --epochs 300 --cv_epoch 20 --patience 10 --use_cv True
  • BANK
    CUDA_VISIBLE_DEVICES=0 python  --dx 8 --dy 17 --train True --data uci_BANK --epochs 300 --cv_epoch 20 --patience 10 --use_cv True
    CUDA_VISIBLE_DEVICES=0 python  --dx 20 --dy 90 --train True --data uci_YPMSD --epochs 300 --cv_epoch 20 --patience 10 --use_cv True

Image Datasets

MNIST and CIFAR-10 were used in our study. Unlike previous experiments, we focus on conditional density estimation where a ont-hot encoded class label will be introduced to the networks as an additional input.

Download data from zenodo repository and uncompress the two datasets under data folder.

One can run the conditional image generation and conditional denstiy estimation simultaneously through the following script.


    Model training

    CUDA_VISIBLE_DEVICES=0 python  --dx 100 --dy 784 --train True --data mnist --epochs 100 --cv_epoch 50 --patience 5

    Model test

    python --data mnist --path path
    [path] -- path to data folder (e.g., data/density_est_YYYYMMDD_HHMMSS_mnist_x_dim=100_y_dim=784_alpha=10.0_beta=10.0)
  • CIFAR-10

    Model training

    CUDA_VISIBLE_DEVICES=0 python  --dx 100 --dy 3072 --train True --data cifar10 --epochs 1000 --cv_epoch 500 --patience 5

    Model test

    python --data cifar10 --path path

After model test, the generated images can be found in the first part of outputs.

Outlier Detection

We introduced three outlier detection datasets (Shuttle, Mammography, and ForestCover) from ODDS library. Download the three datasets (ODDS.tar.gz) from the zenodo repository. Uncompress it under the datasets folder.

One can run the following commonds to train a Roundtrip model and evaluate by precision at K.

  • Shuttle

    Model training

    CUDA_VISIBLE_DEVICES=0 python  --dx 3 --dy 9 --train True --data odds_Shuttle --epochs 300 --cv_epoch 30 --patience 10

    Model evaluation

    python --data odds_Shuttle --epoch epoch --path path
    [epoch] -- epoch for loading model weights (e.g., epoch recorded in the last line in log_test.txt)
    [path] -- path to the frist part of outputs (e.g., data/density_est_YYYYMMDD_HHMMSS_odds_Shuttle_x_dim=3_y_dim=9_alpha=10.0_beta=10.0)
  • Mammography

    Model training

    CUDA_VISIBLE_DEVICES=0 python --dx 3 --dy 6 --train True --data odds_Mammography --epochs 300 --cv_epoch 30 --patience 10

    Model evaluation

    python --data odds_Mammography --epoch epoch --path path
  • ForestCover

    Model training

    CUDA_VISIBLE_DEVICES=0 python --dx 4 --dy 10 --train True --data odds_ForestCover --epochs 300 --cv_epoch 30 --patience 10

    Model evaluation

    python --data odds_ForestCover --epoch epoch  --path path

The precision at K of Roundtrip, One-class SVM and Isolation Forest will be calculated and printed.

Pretrain Models

We provide various of pretrain models for a quick implementation of Roundtrip. First, one needs to download the pretrain models pre_trained_models.tar.gz from zenodo repository. Then uncompress it under Roundtrip folder. For the above models that use for model evaluation. One can simply add --pretrain True to the end of each evaluation command. For an example, one can run

python --data mnist --path path --pretrain True

This can implement the Beyes posterior probability estimation, which will result in around 98.3% classification accuracy. Note that in pretrain evaluation, the path parameter can be any fold path like density_est_YYYYMMDD_HHMMSS_mnist_x_dim=100_y_dim=784_alpha=10.0_beta=10.0. path name is necessary as it is used for parsing parameters in

Further Application

Roundtrip can be used for a general-purpose density estimation. Besides that, Roundtrip has various downstream applications including but not limited to

  • supervised learning (already covered in this paper)
  • unsupervised learning (refer to our another work published by Nature Machine Intelligence)
  • likelihood-free Bayesian inference
  • sequential Markov chain Monte Carlo (MCMC)


Please feel free to open an issue in Github or directly contact if you have any problem in Roundtrip.


If you find Roundtrip useful for your work, please consider citing our paper:

Qiao Liu, Jiaze Xu, Rui Jiang, Wing Hung Wong. Density estimation using deep generative neural networks[J]. Proceedings of the National Academy of Sciences. 2021, 118 (15) e2101344118; DOI: 10.1073/pnas.2101344118.


This project is licensed under the MIT License - see the file for details


Roundtrip: density estimation with deep generative neural networks




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