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Changing perspective is often a great way to solve burning research problems. Riemannian spaces are such a perspective change, as Arto Klami, an Associate Professor of computer science at the University of Helsinki and member of the Finnish Center for Artificial Intelligence, will tell us in this episode.

He explains the concept of Riemannian spaces, their application in inference algorithms, how they can help sampling Bayesian models, and their similarity with normalizing flows, that we discussed in episode 98.

Arto also introduces PreliZ, a tool for prior elicitation, and highlights its benefits in simplifying the process of setting priors, thus improving the accuracy of our models.

When Arto is not solving mathematical equations, you’ll find him cycling, or around a good board game.

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, Giuliano Cruz, Tim Gasser, James Wade, Tradd Salvo, William Benton, James Ahloy, Robin Taylor,, Chad Scherrer, Zwelithini Tunyiswa, Bertrand Wilden, James Thompson, Stephen Oates, Gian Luca Di Tanna, Jack Wells, Matthew Maldonado, Ian Costley, Ally Salim, Larry Gill, Ian Moran, Paul Oreto, Colin Caprani, Colin Carroll, Nathaniel Burbank, Michael Osthege, Rémi Louf, Clive Edelsten, Henri Wallen, Hugo Botha, Vinh Nguyen, Marcin Elantkowski, Adam C. Smith, Will Kurt, Andrew Moskowitz, Hector Munoz, Marco Gorelli, Simon Kessell, Bradley Rode, Patrick Kelley, Rick Anderson, Casper de Bruin, Philippe Labonde, Michael Hankin, Cameron Smith, Tomáš Frýda, Ryan Wesslen, Andreas Netti, Riley King, Yoshiyuki Hamajima, Sven De Maeyer, Michael DeCrescenzo, Fergal M, Mason Yahr, Naoya Kanai, Steven Rowland, Aubrey Clayton, Jeannine Sue, Omri Har Shemesh, Scott Anthony Robson, Robert Yolken, Or Duek, Pavel Dusek, Paul Cox, Andreas Kröpelin, Raphaël R, Nicolas Rode, Gabriel Stechschulte, Arkady, Kurt TeKolste, Gergely Juhasz, Marcus Nölke, Maggi Mackintosh, Grant Pezzolesi, Avram Aelony, Joshua Meehl, Javier Sabio, Kristian Higgins, Alex Jones, Gregorio Aguilar, Matt Rosinski, Bart Trudeau, Luis Fonseca, Dante Gates, Matt Niccolls, Maksim Kuznecov, Michael Thomas, Luke Gorrie, Cory Kiser and Julio.

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

Takeaways:

- Riemannian spaces offer a way to improve computational efficiency and accuracy in Bayesian inference by considering the curvature of the posterior distribution.

- Riemannian spaces can be used in Laplace approximation and Markov chain Monte Carlo algorithms to better model the posterior distribution and explore challenging areas of the parameter space.

- Normalizing flows are a complementary approach to Riemannian spaces, using non-linear transformations to warp the parameter space and improve sampling efficiency.

- Evaluating the performance of Bayesian inference algorithms in challenging cases is a current research challenge, and more work is needed to establish benchmarks and compare different methods. 

- PreliZ is a package for prior elicitation in Bayesian modeling that facilitates communication with users through visualizations of predictive and parameter distributions.

- Careful prior specification is important, and tools like PreliZ make the process easier and more reproducible.

- Teaching Bayesian machine learning is challenging due to the combination of statistical and programming concepts, but it is possible to teach the basic reasoning behind Bayesian methods to a diverse group of students.

- The integration of Bayesian approaches in data science workflows is becoming more accepted, especially in industries that already use deep learning techniques.

- The future of Bayesian methods in AI research may involve the development of AI assistants for Bayesian modeling and probabilistic reasoning.

Chapters:

00:00 Introduction and Background

02:05 Arto's Work and Background

06:05 Introduction to Bayesian Inference

12:46 Riemannian Spaces in Bayesian Inference

27:24 Availability of Romanian-based Algorithms

30:20 Practical Applications and Evaluation

37:33 Introduction to Prelease

38:03 Prior Elicitation

39:01 Predictive Elicitation Techniques

39:30 PreliZ: Interface with Users

40:27 PreliZ: General Purpose Tool

41:55 Getting Started with PreliZ

42:45 Challenges of Setting Priors

45:10 Reproducibility and Transparency in Priors

46:07 Integration of Bayesian Approaches in Data Science Workflows

55:11 Teaching Bayesian Machine Learning

01:06:13 The Future of Bayesian Methods with AI Research

01:10:16 Solving the Prior Elicitation Problem

Links from the show:

• LBS #29, Model Assessment, Non-Parametric Models, And Much More, with Aki Vehtari: https://learnbayesstats.com/episode/model-assessment-non-parametric-models-aki-vehtari/
• LBS #20 Regression and Other Stories, with Andrew Gelman, Jennifer Hill & Aki Vehtari: https://learnbayesstats.com/episode/20-regression-and-other-stories-with-andrew-gelman-jennifer-hill-aki-vehtari/
• LBS #98 Fusing Statistical Physics, Machine Learning & Adaptive MCMC, with Marylou Gabrié: https://learnbayesstats.com/episode/98-fusing-statistical-physics-machine-learning-adaptive-mcmc-marylou-gabrie/
• Arto’s website: https://www.cs.helsinki.fi/u/aklami/
• Arto on Google Scholar: https://scholar.google.com/citations?hl=en&user=v8PeLGgAAAAJ
• Multi-source probabilistic inference Group: https://www.helsinki.fi/en/researchgroups/multi-source-probabilistic-inference
• FCAI web page: https://fcai.fi
• Probabilistic AI summer school lectures: https://www.youtube.com/channel/UCcMwNzhpePJE3xzOP_3pqsw
• Keynote: "Better priors for everyone" by Arto Klami: https://www.youtube.com/watch?v=mEmiEHsfWyc&ab_channel=ProbabilisticAISchool
• Variational Inference and Optimization I by Arto Klami: https://www.youtube.com/watch?v=60USDNc1nE8&list=PLRy-VW__9hV8s--JkHXZvnd26KgjRP2ik&index=3&ab_channel=ProbabilisticAISchool
• PreliZ, A tool-box for prior elicitation: https://preliz.readthedocs.io/en/latest/
• AISTATS paper that presents the new computationally efficient metric in context of MCMC: https://researchportal.helsinki.fi/en/publications/lagrangian-manifold-monte-carlo-on-monge-patches
• TMLR paper that scales up the solution for larger models, using the metric for sampling-based inference in deel learning: https://openreview.net/pdf?id=dXAuvo6CGI
• Riemannian Laplace approximation (to appear in AISTATS’24): https://arxiv.org/abs/2311.02766
• Prior Knowledge Elicitation -- The Past, Present, and Future: https://projecteuclid.org/journals/bayesian-analysis/advance-publication/Prior-Knowledge-Elicitation-The-Past-Present-and-Future/10.1214/23-BA1381.full

Transcript

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