Agenda

Omiros Papaspiliopoulos
Bocconi University

Abstract

Generalized bi-linear mixed models are the workhorse of applied Statistics and they are used for varied tasks such as small area estimation, item response theory, recommendation and analysis of networks. In modern applications, from political science to electronic marketing, it is common that both the size of the data and the number of random effects are large. As a result, there is an increasing need amongst scientists to have access to inferential and computational frameworks that can cope with large-scale problems and provide reasonable uncertainty quantification.

The posterior dependence in these models is sparse but in an unstructured way that relates to random graphs. As a result, popular inferential approaches and implementations with reasonable uncertainty quantification (such as lmer or INLA), even though highly optimized they eventually have costs that scale polynomially with the size of data and model.

The talk will provide an overview of recent methodologies that have provably linear computational complexity and provide  provably good uncertainty quantification. The methods include collapsed Gibbs samplers, partially factorized variational inference and approximate conjugent gradient Markov chain Monte Carlo. The desired properties are obtained leveraging spectral random graph theory, and a convergence-accuracy duality for variational inference that is of broader interest.

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This lecture is included in the programme of the 2024 ISBA World Meeting

For further information please contact isba2024@unive.it