Gradient Boosted Normalizing Flows

Introduction

The trend in normalizing flow (NF) literature has been to devise deeper, more complex transformations to achieve greater flexibility.

We propose an alternative: Gradient Boosted Normalizing Flows (GBNF) model a density by successively adding new NF components with gradient boosting. Under the boosting framework, each new NF component optimizes a sample weighted likelihood objective, resulting in new components that are fit to the residuals of the previously trained components.

The GBNF formulation results in a mixture model structure, whose flexibility increases as more components are added. Moreover, GBNFs offer a wider, as opposed to strictly deeper, approach that improves existing NFs at the cost of additional training---not more complex transformations.

Link to paper:

Gradient Boosted Normalizing Flows by Robert Giaquinto and Arindam Banerjee. In Advances in Neural Information Processing Systems (NeurIPS), 2020.

Requirements

The code is compatible with:

• pytorch 1.1.0
• python 3.6+ (should work fine with python 2.7 though if you include print_function)

It is recommended that you create a virtual environment with the correct python version and dependencies. After cloning the repository, change directories and run the following codes to create a virtual environment:

python -m venv ./venv
source ./venv/bin/activate
pip install --upgrade pip
pip install -r requirements.txt

(code assumes python refers to python 3.6+, if not use python3)

Data

The experiments can be run on the following images datasets:

• static MNIST: dataset is in data folder;
• OMNIGLOT: the dataset can be downloaded from link;
• Caltech 101 Silhouettes: the dataset can be downloaded from link.
• Frey Faces: the dataset can be downloaded from link.
• CIFAR10: from Torchvision library
• CelebA: from Torchvision library

Additionally, density estimation experiments can be run on datasets from the UCI repository, which can be downloaded by:

./download_datasets.sh

Project Structure

• main_experiment.py: Run experiments for generative modeling with variational autoencoders on image datasets.
• density_experiment.py: Run experiments for density estimation on real datasets.
• toy_experiment.py: Run experiments for the toy datasets for density estimation and matching.
• image_experiment.py: Run experiments for image modeling with only flows (no VAE).
• models: Collection of models implemented in experiments
• optimization: Training, evaluation, and loss functions used in main experiment.
• scripts: Bash scripts for running experiments, along with default configurations used in experiments.
• utils: Utility functions, plotting, and data preparation.
• data: Folder containing raw data.

Getting Started

The scripts folder includes examples for running the GBNF model on the Caltech 101 Silhouettes dataset and a density estimation experiment.

Toy problem: match 2-moons energy function with Boosted Real-NVPs

./scripts/getting_started_toy_matching_gbnf.sh &

Toy problem: density estimation on the 8-Gaussians with Boosted Real-NVPs

./scripts/getting_started_toy_estimation_gbnf.sh &

Density estimation of MINIBOONE dataset with Boosted Glow

./scripts/getting_started_density_estimation_gbnf.sh &

Generative modeling of Caltech 101 Silhouettes images with Boosted Real-NVPs

./scripts/getting_started_vae_gbnf.sh &