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Santa Fe Institute

Maximum Entropy Methods

Santa Fe Institute via Complexity Explorer


Sometimes the best description of a system is one that acknowledges our ignorance. Maximum entropy methods provide a coherent framework for doing this in a rigorous fashion, and their success has been felt in everything from physics to ecology to machine learning.In this tutorial, Simon DeDeo introduces MaxEnt through a series of examples, taking students from the basics of the subject up to its applications in science and engineering. Basic comfort with the use of probabilities, and familiarity with exponentials and logarithms, is required. By the end of the course, students will have a tool for modeling complex systems, and a new set of concepts for thinking about what models are meant to do in the first place.Note that Complexity Explorer tutorials are meant to introduce students to various important techniques and to provide illustrations of their application in complex systems.  A given tutorial is not meant to offer complete coverage of its topic or substitute for an entire course on that topic.   This tutorial is designed for more advanced math students.  Math prerequisites for this course are an understanding of calculus, partial derivatives, shannon entropy; basic probability.Read Simon DeDeo's Q&A about his Maximum Entropy tutorial here.  


  1. Maximum Entropy Methods (Simon DeDeo)
  2. A Simple Example: Waiting for a Taxicab
  3. The Maximum Entropy Method
  4. MaxEnt Applied to the Taxicab Example, Part 1
  5. MaxEnt Applied to the Taxicab Example, Part 2
  6. Review of MaxEnt
  7. A Real-World Example: Modeling the Open Source Ecosystem, Part 1
  8. Modeling the Open Source Ecosystem, Part 2
  9. Modeling the Open Source Ecosystem, Part 3
  10. A Second Real-World Example: Modeling Sears-Roebuck Catalog Prices, Part 1
  11. Modeling Sears-Roebuck Catalog Prices, Part 2
  12. Conclusion
  13. Homework

Taught by

Simon DeDeo


4.6 rating, based on 10 Class Central reviews

Start your review of Maximum Entropy Methods

  • Anonymous
    Awesome course. Loved it. Brilliant teacher. Was just sad it was so short. More please - with more examples and more problems to do!

    Would also love to see a course by this teacher on Lagrangian multipliers with more examples and further development of the geometrical intuitions he gives.
  • Anonymous
    Really excellent course. Appreciate his approach from physics point of view.
    These max entropy distributions reflect how little knowledge we have of the system, but are still able to glean valuable insights. Like the theory of gases, we can't possibly know the trajectories of each gas molecule, but we can talk of an average kinetic energy ...
    Learned a lot from by the Open Source and Sears Roebuck examples.

    Thought maybe this is a better way to introduce physicists to statistical mechanics by going through max entropy introduction.
  • Anonymous
    Quit after the second teaching lecture...

    Although this guy clearly knows what he's talking about - this course is only suitable for stats/physics/mathematics specialist students or higher.

    I am a post-graduate student in the ecology field wanting to understand this topic better, but there are so many assumptions on what you are meant to already know. The language used in this course is not suitable for mathematics novices like myself.

  • Anonymous
    Very interesting, I would have liked to have the scope/limitations of the method of Legrange multipliers explained a little more fully. Also, the possible appendix content about proving that the entropy function has a unique maximum, even subject to constraints, hasn't materialized or I haven't been able to find it.
  • Profile image for Ces Alonso Lobo
    Ces Alonso Lobo
    The most interesting math course I have ever taken. I studied maximum entropy in my degree but what I have learnt in here is much more fundental. I adore the teacher of these lessons, is superclever . He must claim for the Nobel prize in something
  • Teresa Herrero
    A great introduction to the key aspects of Maximum entropy. I could widen my knowledge with the help of more specialized books, thanks to have discovered Its potential through this tutorial.
  • Anonymous
    Excellent introduction to subject. I am interested in understanding patterns in data from a flow cytometer, and this has given me insights, and inspired me to learn about a new subject.
  • Profesor DeDeo is an excellent professor, his explanations in this course are clear and profound. Course of Complexity Explore are extremely useful to develop a research area.
  • Davide Vignoni
    In my opinion, this course is very Interesting, easy to understand and to follow!
    I have learned some mathematical issues that I didn't knew before. Thanks a lot!
  • This really short tutorial should be a must take for anyone interested in modelling. For me it was a game changer in thinking about how to model any physical process.

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