Kernel-Matrix Determinant Estimation from stopped Cholesky Decomposition

This is the code repository for the JMLR article of the same name (pdf).

Requirements

This software has been tested unter Ubuntu 18.04 using Python 3.8.

Installation

Open a terminal in the projects home directory. As a first step, we recommend to create a dedicated python environment. For example, using conda

conda create --prefix ./env
conda activate ./env

Then all pacakges can be installed with the following command:

conda install -y -c conda-forge --file requirements.txt

After that, switch to the openblas folder and run the make command:

cd openblas
make

This may take a while. After that, run

make install PREFIX=../choleskies/openblas/

to complete the installation process.

Troubleshooting

If the make command fails, try make FC=gfortran.

Running Experiments

Open a terminal in the projects home directory. For the fast PUMADYN experiments, run

python run_pumadyn.py

which executes on your local computer.

For the computationally more demanding experiments, our run scripts assume that you are in an environment which allows to send slurm [1] jobs to a cluster. IMPORTANT: the order of the run scripts below is necessary and strictly sequential--only start the next script when the results of all previous results have been obtained.

python run_default_configurations.py
python run_blas_pivoted_configurations.py
python run_blas_stopped_configurations.py

If you want to reproduce the results for the GPyTorch stochastic trace estimator, first install GPyTorch:

conda install -y -c conda-forge --file optional_requirements.txt

then run:

python run_default_ste_configurations.py

Result Generation

Open a terminal in the projects home directory. Run

python make_figures.py
python make_bound_figures.py

from the current folder in a terminal. This may take a while. If you ran the GPyTorch experiments, you can generate the corresponding tikz pictures with

python make_ste_figures.py

To generate a figures.pdf, switch to the tex folder and execute the following five commands (you can speed up make by adding the option -j number_of_cores_you_want_to_dedicate):

cd tex
lualatex figures.tex
make -f figures.makefile
lualatex figures.tex
make -f figures.makefile -B
lualatex figures.tex

Our Results

To use our results, open a terminal in the results folder and run

cat diagonals_part* > diagonals.zip

Then extract diagonals.zip and mlruns.zip in the folder results.

[1] https://slurm.schedmd.com