Episode sponsored by Tidelift: tidelift.com

I bet you already heard of Bayesian nonparametric models, at least on this very podcast. We already talked about Dirichlet Processes with Karin Knudson on episode 4, and then about Gaussian Processes with Elizaveta Semenova on episode 21. Now we’re gonna dive into the mathematical properties of these objects, to understand them better — because, as you may know, Bayesian nonparametrics are quite powerful but also very hard to fit!

Along the way, you’ll learn about probabilistic circuits, sum-product networks and — what a delight — you’ll hear from the Julia community! Indeed, my guest for this episode is no other than… Martin Trapp!

Martin is a core developer of Turing.jl, an open-source framework for probabilistic programming in Julia, and a post-doc in probabilistic machine learning at Aalto University, Finland.

Martin loves working on sum-product networks and Bayesian non-parametrics. And indeed, his research interests focus on probabilistic models that exploit structural properties to allow efficient and exact computations while maintaining the capability to model complex relationships in data. In other words, Martin’s research is focused on tractable probabilistic models.

Martin did his MsC in computational intelligence at the Vienna University of Technology and just finished his PhD in machine learning at the Graz University of Technology. He doesn’t only like to study the tractability of probabilistic models — he also is very found of climbing!

Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work at https://bababrinkman.com/ !

Thank you to my Patrons for making this episode possible!

Yusuke Saito, Avi Bryant, Ero Carrera, Brian Huey, Giuliano Cruz, Tim Gasser, James Wade, Tradd Salvo, Adam Bartonicek, William Benton, Alan O'Donnell, Mark Ormsby, Demetri Pananos, James Ahloy, Jon Berezowski, Robin Taylor, Thomas Wiecki, Chad Scherrer, Vincent Arel-Bundock, Nathaniel Neitzke, Zwelithini Tunyiswa, Elea McDonnell Feit, Bertrand Wilden, James Thompson, Stephen Oates, Gian Luca Di Tanna, Jack Wells, Matthew Maldonado, Ian Costley, Ally Salim, Larry Gill, Joshua Duncan, Ian Moran, Paul Oreto, Colin Caprani, George Ho, Colin Carroll, Nathaniel Burbank, Michael Osthege, Rémi Louf, Clive Edelsten, Henri Wallen, Jonathan Sedar, Hugo Botha, Vinh Nguyen and Raul Maldonado.

Visit https://www.patreon.com/learnbayesstats to unlock exclusive Bayesian swag ;)

Links from the show:

• Martin's website: https://trappmartin.github.io/
• Martin on GitHub: https://github.com/trappmartin
• Martin on Twitter: https://twitter.com/martin_trapp
• Turing, Bayesian inference with Julia: https://turing.ml/dev/
• Hierarchical Dirichlet Processes: https://people.eecs.berkeley.edu/~jordan/papers/hdp.pdf
• The Automatic Statistician: https://www.doc.ic.ac.uk/~mpd37/teaching/2014/ml_tutorials/2014-01-29-slides_zoubin2.pdf
• Truncated Random Measures: https://arxiv.org/abs/1603.00861
• Deep Structured Mixtures of Gaussian Processes: https://arxiv.org/abs/1910.04536
• Probabilistic Circuits -- Representations, Inference, Learning and Theory: https://www.youtube.com/watch?v=2RAG5-L9R70
• Applied Stochastic Differential Equations, from Simo Särkkä and Arno Solin: https://users.aalto.fi/~asolin/sde-book/sde-book.pdf