A PyTorch implementation of Bezier simplex fitting.

The Bezier simplex is a high-dimensional generalization of the Bezier curve. It enables us to model a complex-shaped point cloud as a parametric hyper-surface in high-dimensional spaces. This package provides an algorithm to fit a Bezier simplex to given data points. To process terabyte-scale data, this package supports distributed training, realtime progress reporting, and checkpointing on top of PyTorch Lightning and MLflow.

See the following papers for technical details.

• Kobayashi, K., Hamada, N., Sannai, A., Tanaka, A., Bannai, K., & Sugiyama, M. (2019). Bézier Simplex Fitting: Describing Pareto Fronts of´ Simplicial Problems with Small Samples in Multi-Objective Optimization. Proceedings of the AAAI Conference on Artificial Intelligence, 33(01), 2304-2313. https://doi.org/10.1609/aaai.v33i01.33012304
• Tanaka, A., Sannai, A., Kobayashi, K., & Hamada, N. (2020). Asymptotic Risk of Bézier Simplex Fitting. Proceedings of the AAAI Conference on Artificial Intelligence, 34(03), 2416-2424. https://doi.org/10.1609/aaai.v34i03.5622

Python >=3.8, <3.12.

Download the latest Miniconda and install it. Then, install MLflow on your conda environment:

conda install -c conda-forge mlflow

Prepare data:

cat <<EOS > params.csv
1.00, 0.00
0.75, 0.25
0.50, 0.50
0.25, 0.75
0.00, 1.00
EOS
cat <<EOS > values.csv
0.00, 1.00
3.00, 2.00
4.00, 5.00
7.00, 6.00
8.00, 9.00
EOS

Run the following command:

mlflow run https://github.com/rafcc/pytorch-bsf \
  -P params=params.csv \
  -P values=values.csv \
  -P degree=3

which automatically sets up the environment and runs an experiment:

1. Download the latest pytorch-bsf into a temporary directory.
2. Create a new conda environment and install dependencies in it.
3. Run an experiment on the temporary directory and environment.

pip install pytorch-bsf

This package provides a command line interface to train a Bezier simplex with a dataset file.

Execute the torch_bsf module:

python -m torch_bsf \
  --params=params.csv \
  --values=values.csv \
  --degree=3

Train a model by fit(), and call the model to predict.

import torch
import torch_bsf

# Prepare training data
ts = torch.tensor(  # parameters on a simplex
    [
        [8 / 8, 0 / 8],
        [7 / 8, 1 / 8],
        [6 / 8, 2 / 8],
        [5 / 8, 3 / 8],
        [4 / 8, 4 / 8],
        [3 / 8, 5 / 8],
        [2 / 8, 6 / 8],
        [1 / 8, 7 / 8],
        [0 / 8, 8 / 8],
    ]
)
xs = 1 - ts * ts  # values corresponding to the parameters

# Train a model
bs = torch_bsf.fit(params=ts, values=xs, degree=3)

# Predict by the trained model
t = [
    [0.2, 0.8],
    [0.7, 0.3],
]
x = bs(t)
print(f"{t} -> {x}")

See documents for more details. https://rafcc.github.io/pytorch-bsf/

RIKEN AIP-FUJITSU Collaboration Center (RAFCC)

MIT