... and a short blog post with some additional details.

🌎 statmodeling.stat.columbia.edu/2025/11/07/m...

Details and Q&A for applications:
www.stat.ubc.ca/graduate-adm...

I also like to describe this paper as a discussion on what is the best circle to approximate an ellipse :)

🧵 4/4

This paper contributes to the foundational theory of VI, and dives deep into both conceptual and practical questions such as: How do we measure uncertainty in high-dimensions? How should we measure discrepancy between probability distributions?

🧵 3/

The two main results of the paper are:
1️⃣ An impossibility theorem that shows that any factorized (mean-field) approximation of VI can at beast learn one of three measures of uncertainty
2️⃣ An ordering of divergences used as objectives for VI based on the uncertainty in their approximation.

🧵 2/

💻 This was also my first time using Stan playground (github.com/flatironinst...) to teach a class! Thank you Brian Ward for creating this tool and helping me set it up for the class!

📔 My course: "Bayesian Statistics: a practical introduction." We covered Bayesian models (priors and likelihoods), Markov chain Monte Carlo and uncertainty aware cross-validation. Most of our discussion was motivated by an example from epidemiology.

👨‍💻 Credit also to Brian Ward and Steve Bronder for their contribution to the C++ implementation and integration with the Stan ecosytem. (From what I understand, WALNUTS is not part of the next Stan release but you can use it on models written in Stan!!)

🙏This award is this much more meaningful to me in that it celebrates my collaboration with the amazing Lawrence Saul (users.flatironinstitute.org/~lsaul/).

💡We provide theory on VI's ability to recover certain statistics, despite misspecification---that is in settings where we do NOT drive the KL-divergence to 0.

👉 VI is provably good at recovering the mean and correlation matrix.