Scalable inference for crossed random effects models

Müller, Maximilian

Scalable inference for crossed random effects models

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Müller, M. Scalable inference for crossed random effects models. 2020. handle: http://hdl.handle.net/10230/46310

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Abstract

In order to apply statistical learning in the framework of crossed random effects models it is necessary to efficiently compute the Cholesky factor L of the models precision matrix. In this paper we show that for the case of 2 factors the crucial point to this end is not only the sparsity of L, but also the arrangement of non-zero entries. In particular, we express the number of flops required for the calculation of L by the number of 3-cycles in the corresponding graph. We then introduce specific designs of 2-factor crossed random effects models for which we can prove sparsity and density, respectively. We confirm our results by numerical studies with the R-packages Spam and Matrix and find hints that approximations of the Cholesky factor could be an interesting approach for further decrease of the cost of computing L.