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MadMiner: Machine learning–based inference for particle physics

By Johann Brehmer, Felix Kling, Irina Espejo, Sinclert Pérez, and Kyle Cranmer

PyPI version Build Status Documentation Status Gitter Code style: black License: MIT DOI arXiv


Schematics of the simulation and inference workflow

Particle physics processes are usually modeled with complex Monte-Carlo simulations of the hard process, parton shower, and detector interactions. These simulators typically do not admit a tractable likelihood function: given a (potentially high-dimensional) set of observables, it is usually not possible to calculate the probability of these observables for some model parameters. Particle physicisists usually tackle this problem of "likelihood-free inference" by hand-picking a few "good" observables or summary statistics and filling histograms of them. But this conventional approach discards the information in all other observables and often does not scale well to high-dimensional problems.

In the three publications "Constraining Effective Field Theories With Machine Learning", "A Guide to Constraining Effective Field Theories With Machine Learning", and "Mining gold from implicit models to improve likelihood-free inference", a new approach has been developed. In a nutshell, additional information is extracted from the simulations that is closely related to the matrix elements that determine the hard process. This "augmented data" can be used to train neural networks to efficiently approximate arbitrary likelihood ratios. We playfully call this process "mining gold" from the simulator, since this information may be hard to get, but turns out to be very valuable for inference.

But the gold does not have to be hard to mine: MadMiner automates these modern multivariate inference strategies. It wraps around the simulators MadGraph and Pythia, with different options for the detector simulation. It streamlines all steps in the analysis chain from the simulation to the extraction of the augmented data, their processing, the training and evaluation of the neural networks, and the statistical analysis are implemented.



Our main publication MadMiner: Machine-learning-based inference for particle physics provides an overview over this package. We recommend reading it first before jumping into the code.

Installation instructions

Please have a look at our installation instructions.


In the examples folder in this repository, we provide two tutorials. The first at examples/tutorial_toy_simulator/tutorial_toy_simulator.ipynb is based on a toy problem rather than a full particle-physics simulation. It demonstrates inference with MadMiner without spending much time on the more technical steps of running the simulation. The second, at examples/tutorial_particle_physics, shows all steps of a particle-physics analysis with MadMiner.

These examples are the basis of an online tutorial built with on Jupyter Books. It also walks through how to run MadMiner using docker so that you don't have to install Fortran, MadGraph, Pythia, Delphes, etc. You can even run it with no install using binder.


The madminer API is documented on readthedocs.


If you have any questions, please chat to us in our Gitter community or write us at


If you use MadMiner, please cite our main publication,

      author         = "Brehmer, Johann and Kling, Felix and Espejo, Irina and
                        Cranmer, Kyle",
      title          = "{MadMiner: Machine learning-based inference for particle
      journal        = "Comput. Softw. Big Sci.",
      volume         = "4",
      year           = "2020",
      number         = "1",
      pages          = "3",
      doi            = "10.1007/s41781-020-0035-2",
      eprint         = "1907.10621",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-ph",
      SLACcitation   = "%%CITATION = ARXIV:1907.10621;%%"

The code itself can be cited as

      author         = "Brehmer, Johann and Kling, Felix and Espejo, Irina and Cranmer, Kyle",
      title          = "{MadMiner}",
      doi            = "10.5281/zenodo.1489147",
      url            = {}

The main references for the implemented inference techniques are the following:


We are immensely grateful to all contributors and bug reporters! In particular, we would like to thank Zubair Bhatti, Philipp Englert, Lukas Heinrich, Alexander Held, Samuel Homiller, and Duccio Pappadopulo.

The SCANDAL inference method is based on Masked Autoregressive Flows, and our implementation is a PyTorch port of the original code by George Papamakarios et al., which is available at Our was adapted from

iris-hep logo

We are grateful for the support of iris-hep and diana-hep.


An inference toolkit for LHC measurements







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