Abstract While generalized linear mixed models are a fundamental tool in applied statistics, many specifications, such as those involving categorical factors with many levels or interaction terms, can be computationally challenging to estimate due to the need to compute or approximate high-dimensional integrals. Variational inference is a popular way to perform such computations, especially in the Bayesian context. However, naive use of such methods can provide unreliable uncertainty quantification. We show that this is indeed the case for mixed models, proving that standard mean-field variational inference dramatically underestimates posterior uncertainty in high-dimensions. We then show how appropriately relaxing the mean-field assumption leads to methods whose uncertainty quantification does not deteriorate in high-dimensions, and whose total computational cost scales linearly with the number of parameters and observations. Our theoretical and numerical results focus on mixed models with Gaussian or binomial likelihoods, and rely on connections to random graph theory to obtain sharp high-dimensional asymptotic analysis. We also provide generic results, which are of independent interest, relating the accuracy of variational inference to the convergence rate of the corresponding coordinate ascent algorithm that is used to find it. Our proposed methodology is implemented in the R package vglmer. Numerical results with simulated and real data examples illustrate the favourable computation cost versus accuracy trade-off of our approach compared to various alternatives.

M Goplerud

O Papaspiliopoulos

G Zanella

Biometrika

BIOMETRIKA 主要是一本统计学杂志，其中重点放在包含在应用中具有直接或潜在价值的原始理论贡献的论文上。不时还会发表一些边缘领域的论文。

Biometrika is a journal primarily focused on statistics, particularly papers that present original theoretical contributions with direct or potential value in applications. Occasionally, it also publishes research from peripheral areas.

《Biometrika》是一本主要关注统计学的期刊，特别是那些在应用中具有直接或潜在价值的原创理论贡献的论文。此外，期刊偶尔也会发表一些边缘领域的研究成果。

Category	Quartile
数学	2
数学, 数学与计算生物学	1
数学, 生物学	2
数学, 统计学与概率论	2

Partially factorized variational inference for high-dimensional mixed models

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Journal Info

Category	Quartile
STATISTICS & PROBABILITY	1