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arXiv Venue Project Status: Active – The project has reached a stable, usable state and is being actively developed. PyPI Latest Release build Code style: black

Benchmarking Mutual Information

BMI is the package for estimation of mutual information between continuous random variables and testing new estimators.

Getting started

While we recommend taking a look at the documentation to learn about full package capabilities, below we present the main capabilities of the Python package. (Note that BMI can also be used to test non-Python mutual information estimators.)

You can install the package using:

$ pip install benchmark-mi

Alternatively, you can use the development version from source using:

$ pip install "bmi @ https://github.com/cbg-ethz/bmi"

Note: BMI uses JAX and by default installs the CPU version of it. If you have a device supporting CUDA, you can install the CUDA version of JAX.

Now let's take one of the predefined distributions included in the benchmark (named "tasks") and sample 1,000 data points. Then, we will run two estimators on this task.

import bmi

task = bmi.benchmark.BENCHMARK_TASKS['1v1-normal-0.75']
print(f"Task {task.name} with dimensions {task.dim_x} and {task.dim_y}")
print(f"Ground truth mutual information: {task.mutual_information:.2f}")

X, Y = task.sample(1000, seed=42)

cca = bmi.estimators.CCAMutualInformationEstimator()
print(f"Estimate by CCA: {cca.estimate(X, Y):.2f}")

ksg = bmi.estimators.KSGEnsembleFirstEstimator(neighborhoods=(5,))
print(f"Estimate by KSG: {ksg.estimate(X, Y):.2f}")

Evaluating a new estimator

The above code snippet may be convenient for estimating mutual information on a given data set or for the development of a new mutual information estimator. However, for extensive benchmarking it may be more convenient to use one of the benchmark suites available in the workflows/benchmark/ subdirectory.

For example, you can install Snakemake and run a small benchmark suite on several estimators using:

$ snakemake -c4 -s workflows/benchmark/demo/run.smk

In about a minute it should generate minibenchmark results in the generated/benchmark/demo directory. Note that the configuration file, workflows/benchmark/demo/config.py, explicitly defines the estimators and tasks used, as well as the number of samples.

Hence, it is easy to benchmark a custom estimator by importing it and including it in the configuration dictionary. More information is available here, where we cover evaluating new Python as well as non-Python estimators.

Similarly, it is easy to change the number of samples or adjust the tasks included in the benchmark. We defined several benchmark suites with shared structure.

List of implemented estimators

(Your estimator can be here too! Please, reach out to us if you would like to contribute.)

Citing

✨ New! ✨ On the properties and estimation of pointwise mutual information profiles

arXiv

In this manuscript we discuss the pointwise mutual information profile, an invariant which can be used to diagnose limitations of the previous mutual information benchmark, and a flexible distribution family of Bend and Mix Models. These distributions can be used to create more expressive benchmark tasks and provide model-based Bayesian estimates of mutual information.

Workflows:

@article{pmi-profiles-2023,
   title={On the properties and estimation of pointwise mutual information profiles},
   author = {Czy\.{z}, Pawe{\l}  and Grabowski, Frederic and Vogt, Julia and Beerenwinkel, Niko and Marx, Alexander},
   journal={arXiv preprint arXiv:2310.10240},
   year={2023}
}

Beyond normal: On the evaluation of the mutual information estimators

arXiv Venue Manuscript

In this manuscript we discuss a benchmark for mutual information estimators.

Workflows:

@inproceedings{beyond-normal-2023,
 title = {Beyond Normal: On the Evaluation of Mutual Information Estimators},
 author = {Czy\.{z}, Pawe{\l}  and Grabowski, Frederic and Vogt, Julia and Beerenwinkel, Niko and Marx, Alexander},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {A. Oh and T. Neumann and A. Globerson and K. Saenko and M. Hardt and S. Levine},
 pages = {16957--16990},
 publisher = {Curran Associates, Inc.},
 url = {https://proceedings.neurips.cc/paper_files/paper/2023/file/36b80eae70ff629d667f210e13497edf-Paper-Conference.pdf},
 volume = {36},
 year = {2023}
}