Faster ICA by preconditioning with Hessian approximations

This repository hosts several second order algorithms to solve maximum likelihood ICA.

The algorithms can be found in ml_ica/algorithms. They are:

• Picard (Preconditioned ICA for Real Data): A preconditioned L-BFGS algorithm. The fastest algorithm in the repository.
• Simple Quasi-Newton method <https://ie.technion.ac.il/~mcib/newt_ica_ica2003.pdf>_.
• Relative Trust region method <https://pdfs.semanticscholar.org/7f78/929ebd3e7f53d3597adda117a80bbd0f852a.pdf>_.
• Truncated Newton method <http://ieeexplore.ieee.org/document/7952614/>_.

These algorithms have all been rewritten in Python. They call the same gradient, Hessian and likelihood functions, which makes time comparison meaningful.

The algorithms come with a benchmark at ml_ica/example/benchmark.py. This script runs each algorithm on the same real dataset (fMRI or EEG) and times it.

Installation

Clone the repository::

$ git clone https://github.com/pierreablin/faster-ica.git $ cd faster-ica $ pip install -e .

The easiest way to get started is to run the benchmark::

$ python examples/benchmark.py

Dependencies

These are the dependencies to run the algorithms:

• numpy (>=1.8)
• matplotlib (>=1.3)
• numexpr (>= 2.0)
• scipy (>=0.19)

Cite

If you use this code in your project, please cite this paper <https://arxiv.org/abs/1706.08171>_::

Pierre Ablin, Jean-Francois Cardoso, and Alexandre Gramfort
Faster independent component analysis by preconditioning with Hessian approximations
Arxiv preprint, 2017