Legendre decomposition implementation

This project contains the following three python implementation of Legendre decomposition and Many-body Approximation for Non-negative Tensors.

• Naïve implementation:

  • straightforward implementation by using SciPy/NumPy

• Faster implementation:

  • Vectorization using equivalent NumPy code

• GPU implementation:

  • Using CuPy to further change NumPy code to GPU-executable code
  • The same method is used for the Faster implementation and GPU, and switching is done by enabling or disabling the GPU.

Installation

Installation of pyLegendreDecomposition

pip install git+https://github.com/kojima-r/pyLegendreDecomposition.git

Installation of Cupy

pip install  cupy-cuda12x

Please change the cuda12x as appropriate. See the cupy manual for details.

https://docs.cupy.dev/en/stable/install.html

Simple Usage

from legendre_decomp import LD
all_history_kl,scaleX,Q,Hq = LD(X,order=2)

• X: a original input tensor
• order: an order parameter of many-body approximation
• all_history_kl: KL divergence history
• scaleX: Scaled X tensor
• Q: Q tensor
• theta: Theta

See API reference of LD for details.

Documents / notebook

API reference

Benchmark results

Colaboratory notebook

Project structure

• legendre_decomp: Main module
• docs: Documentation
• tests: Functional tests
• scripts: Benchmark scripts
• notebooks: Benchmark Jupyter Notebooks

Reference

Many-body Approximation for Non-negative Tensors: https://arxiv.org/abs/2209.15338

@article{ghalamkari2024many,
  title={Many-body Approximation for Non-negative Tensors},
  author={Ghalamkari, Kazu and Sugiyama, Mahito and Kawahara, Yoshinobu},
  journal={Advances in Neural Information Processing Systems},
  volume={36},
  year={2024}
}

Legendre Decomposition for Tensors: https://arxiv.org/abs/1802.04502

@article{sugiyama2018legendre,
  title={Legendre decomposition for tensors},
  author={Sugiyama, Mahito and Nakahara, Hiroyuki and Tsuda, Koji},
  journal={Advances in Neural Information Processing Systems},
  volume={31},
  year={2018}
}

How to build documentation (need sphinx)

Installation of sphinx modules

pip install sphinx-autoapi
pip install pydata-sphinx-theme

Building documents

sphinx-build -M html docs/source docs/build

or

cd docs
make html

The documentation including installation manual can then be accessed from docs/build/html/index.html