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Gaussianization Flows

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Description

This project features some exploration to get a fully parameterized Gaussianization scheme. There is a big normalizing flows community with many different algorithms for density estimation and sampling. There is also a relatively small community using Gaussianization and density destructors for other applications including information theory measures. This is an attempt to bridge the two communities together.

References

This project was inspired by:

• RBIG - original algorithm
• Gaussianization Flows - the fully parameterized method.
• nflows - the research normalizing flows library.

Demos

• Original Exploration -

1D Example

Here is an example where we show the original data and the data generated by a trained Gaussianization Flow model.

| Original Data | Generated Samples | | :--------------------------------------------: | :-------------------------------------------: | | | |

The same Gaussianization Flow model with the initial Latent space versus the latent space after trained.

| Original Latent Space | Trained Latent Space | | :-------------------------------------------: | :----------------------------------------------: | | | |

2D Example

Here is an example where we show the original data and the data generated by a trained Gaussianization Flow model.

| Original Data | Generated Samples | | :--------------------------------------------------------: | :-------------------------------------------------------: | | | |

...and the probabilities of the dataset.

| Original Data | | :-------------------------------------------------: | | |

The same Gaussianization Flow model with the initial Latent space versus the latent space after trained.

| Original Latent Space | Trained Latent Space | | :-------------------------------------------------------: | :----------------------------------------------------------: | | | |

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Acknowledgements

This work was supported by the European Research Council (ERC) Synergy Grant “Understanding and Modelling the Earth System with Machine Learning (USMILE)” under Grant Agreement No 855187.