Machine Learning Coffee seminar: "Eco-friendly Bayes: reusing computationally costly posteriors in post-hoc analyses" Paul Blomstedt

Weekly seminars held jointly by Aalto University and the University of Helsinki.

Helsinki region machine learning researchers will start our week by an exciting machine learning talk. The aim is to gather people from different fields of science with interest in machine learning. Porridge and coffee is served at 9:00 and the talk will begin at 9:15. The venue for this talk is seminar room T5, CS building.

Subscribe to the mailing list where seminar topics are announced beforehand.

Eco-friendly Bayes: reusing computationally costly posteriors in post-hoc analyses

Paul Blomstedt
Department of Computer Science, Aalto University

Abstract:

Bayesian inference has many attractive features, but a major challenge is its potentially very high computational cost. While sampling from the prior distribution is often straightforward, the most expensive part is typically conditioning on the data. In many problems, a single data set data may not be informative enough to enable reliable inference for a given quantity of interest. This can be difficult to assess in advance and may require a considerable amount of computation to discover, resulting in a weakly informative posterior distribution "gone to waste". On the other hand, borrowing strength across multiple related data sets using a hierarchical model may for very costly models be computationally infeasible.

As an alternative approach to traditional hierarchical models, we develop in this work a framework which reuses and combines posterior distributions computed on individual data sets to achieve post-hoc borrowing of strength, without the need to re-do expensive computations on the data. As a by-product, we also obtain a notion of meta-analysis for posterior distributions. By adopting the view that posterior distributions are beliefs which reflect the uncertainty about the value of some quantity, we formulate our approach as Bayesian inference with uncertain observations. We further show that this formulation is closely related to belief propagation. Finally, we illustrate the framework with post-hoc analyses of likelihood-free Bayesian inferences.

**

See the next talks at the seminar webpage.

Please spread the news and join us for our weekly habit of beginning the week by an interesting machine learning talk!

Welcome!