# Fast and Accurate Estimation of Non-Nested Binomial Hierarchical Models Using Variational Inference

@article{Goplerud2020FastAA, title={Fast and Accurate Estimation of Non-Nested Binomial Hierarchical Models Using Variational Inference}, author={Max Goplerud}, journal={arXiv: Methodology}, year={2020} }

Estimating non-linear hierarchical models can be computationally burdensome in the presence of large datasets and many non-nested random effects. Popular inferential techniques may take hours to fit even relatively straightforward models. This paper provides two contributions to scalable and accurate inference. First, I propose a new mean-field algorithm for estimating logistic hierarchical models with an arbitrary number of non-nested random effects. Second, I propose "marginally augmentedâ€¦Â Expand

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#### References

SHOWING 1-10 OF 66 REFERENCES

Variational Inference for Generalized Linear Mixed Models Using Partially Noncentered Parametrizations

- Mathematics
- 2013

The effects of different parametrizations on the convergence of Bayesian computational algorithms for hierarchical models are well explored. Techniques such as centering, noncentering and partialâ€¦ Expand

Fast and Accurate Binary Response Mixed Model Analysis via Expectation Propagation

- Computer Science, Mathematics
- Journal of the American Statistical Association
- 2019

Numerical studies reveal the availability of fast, highly accurate and scalable methodology for binary mixed model analysis and show that fast and accurate quadrature-free inference can be realized for the probit link case with multivariate random effects and higher levels of nesting. Expand

Semi-Implicit Variational Inference

- Mathematics, Computer Science
- ICML
- 2018

With a substantially expanded variational family and a novel optimization algorithm, SIVI is shown to closely match the accuracy of MCMC in inferring the posterior in a variety of Bayesian inference tasks. Expand

Weakly Informative Prior for Point Estimation of Covariance Matrices in Hierarchical Models

- Mathematics
- 2015

When fitting hierarchical regression models, maximum likelihood (ML) estimation has computational (and, for some users, philosophical) advantages compared to full Bayesian inference, but when theâ€¦ Expand

A Variational Maximizationâ€“Maximization Algorithm for Generalized Linear Mixed Models with Crossed Random Effects

- Mathematics, Medicine
- Psychometrika
- 2017

Numerical studies show that under the small sample size conditions that are considered the proposed variational maximizationâ€“maximization algorithm outperforms the Laplace approximation. Expand

Streamlined Variational Inference for Linear Mixed Models with Crossed Random Effects

- Mathematics
- 2019

We derive streamlined mean field variational Bayes algorithms for fitting linear mixed models with crossed random effects. In the most general situation, where the dimensions of the crossed groupsâ€¦ Expand

Bayesian Inference for Logistic Models Using PĂłlyaâ€“Gamma Latent Variables

- Computer Science, Mathematics
- 2012

We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of PĂłlyaâ€“Gamma distributions, which are constructedâ€¦ Expand

Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC

- Computer Science, Mathematics
- Stat. Comput.
- 2017

An efficient computation of LOO is introduced using Pareto-smoothed importance sampling (PSIS), a new procedure for regularizing importance weights, and it is demonstrated that PSIS-LOO is more robust in the finite case with weak priors or influential observations. Expand

Gaussian Variational Approximate Inference for Generalized Linear Mixed Models

- Mathematics
- 2012

Variational approximation methods have become a mainstay of contemporary machine learning methodology, but currently have little presence in statistics. We devise an effective variationalâ€¦ Expand

The one-step-late PXEM algorithm

- Mathematics, Computer Science
- Stat. Comput.
- 2003

The one-step-late EM algorithm is adapted to PXEM to establish a fast closed form algorithm that improves on the one- Step-Late EM algorithm by insuring monotone convergence, and is used to fit a probit regression model and a variety of dynamic linear models. Expand