https://github.com/ryushinn/flows-on-sphere

This is a Pytorch implementation of [normalizing flows on tori and spheres, ICML 2020]
https://github.com/ryushinn/flows-on-sphere

distribution-estimation manifolds normalizing-flows

Last synced: about 1 month ago
JSON representation

This is a Pytorch implementation of [normalizing flows on tori and spheres, ICML 2020]

• Host: GitHub
• URL: https://github.com/ryushinn/flows-on-sphere
• Owner: ryushinn
• License: mit
• Created: 2022-06-26T23:14:30.000Z (over 2 years ago)
• Default Branch: main
• Last Pushed: 2022-10-12T12:45:55.000Z (about 2 years ago)
• Last Synced: 2023-03-22T08:27:53.540Z (almost 2 years ago)
• Topics: distribution-estimation, manifolds, normalizing-flows
• Language: Python
• Homepage:
• Size: 302 KB
• Stars: 9
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

Awesome Lists containing this project

README

        
# Overview

This is a Pytorch implementation of [Normalizing Flows on Tori and Spheres](https://arxiv.org/abs/2002.02428) by Rezende et al. All 3 flows on spheres MS, EMP, and EMSRE are implemented, and the Table.1 results have been reproduced. 

This is another great and helpful [JAX attempt](https://github.com/katalinic/sdflows) I refered though the experiment of (N=24, K=1) fails in their case.

# Experiments

We conduct the experiments reported in the Table.1 in the paper, and compare results below (theirs/ours):

## Quantitative

| Model                       | KL          | ESS       |

| --------------------------- | ----------- | --------- |

| MS  | 0.05 / 0.03 | 90% / 96% |

| EMP                | 0.50 / 0.59 | 43% / 42% |

| EMSRE        | 0.82 / 0.81 | 42% / 48% |

| EMSRE         | 0.19 / 0.19 | 75% / 82% |

| EMSRE        | 0.10 / 0.16 | 85% / 84% |

## Qualitative

|  Tagrgt Density   |   Approximated Density by MS  |  Approximated Density by EMSRE   |  Approximated Density by EMP    |

| --- | --- | --- | --- |

|   |     |     |     |

# Run

```bash

pip install -r requirements.txt

# run MS

python MS.py --N 1 --Km 12 --Ks 32

# run EMSRE

python EMSRE --N 24 --K 1

# run EMP

python EMP.py --N 1

```

# Some derivations

1. The gradient of spline transforms: check the paper [Neural Spline Flows](https://proceedings.neurips.cc/paper/2019/hash/7ac71d433f282034e088473244df8c02-Abstract.html)

2. The gradient of mobius transforms :

Note that we only want the determinant of the gradient . 

As the mobius transform  maps a point in a circle into another point in the circle, 

we can have: