Por Omiros Papaspiliopoulos, (Department of Decision Sciences, Bocconi University).
Mixed models are the workhorse of applied Statistics. We are interested in models with additive and multiplicative interactions between random effects and this generates a broad framework that is routinely used for varied tasks such as small area estimation, item response theory, recommender systems and analysis of networks. Two structural properties of these models are a sparse Gaussian distribution for the random effects and a (typically) sparse design matrix.
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, hence it is crucial that the cost of computational methods for inference scale scales linearly with respect to those. However, the sparsity in such models is such that popular implementations, such as those in lmer or INLA have polynomial costs. We adopt a Bayesian approach (although the essence of our arguments applies more generally) for inference and design families of variational approximations with provable scalability and guarantees for the resultant approximation error.
In the talk, I will give an accessible introduction to the models and their applications, and to variational inference and will provide some highlights of our main results.
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