Streamlined Variational Inference with Higher Level Random Effects
Authors: Tui H. Nolan, Marianne Menictas, Matt P. Wand
JMLR 2020 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | To assess finite sample performance, we obtained timing results for simulated data according to a version of model (7) for which both the fixed effects and random effects had dimension 2...The number of groups varied over m {200, 400, 600, 800, 1000} and 100 replications were simulated for each value of m...We now provide illustration for data from the Collaborative Perinatal Project, a large longitudinal perinatal health study that was run in the United States of America during 1959 1974 (e.g. Klebanoff, 2009). |
| Researcher Affiliation | Academia | Tui H. Nolan EMAIL School of Mathematical and Physical Sciences University of Technology Sydney...Marianne Menictas EMAIL School of Mathematical and Physical Sciences University of Technology Sydney...Matt P. Wand EMAIL School of Mathematical and Physical Sciences University of Technology Sydney |
| Pseudocode | Yes | Algorithm 1 QR-decomposition-based streamlined algorithm for obtaining mean field variational Bayes approximate posterior density functions for the parameters in the two-level linear mixed model (7) with product density restriction (8)...Algorithm A.1 The Solve Two Level Sparse Matrix algorithm for solving the two-level sparse matrix problem x = A 1a and sub-blocks of A 1 corresponding to the non-zero sub-blocks of A. |
| Open Source Code | No | The first phase of the study involved comparing the computational times of the streamlined Algorithm 1 with its na ıve counterpart for which (10) was implemented directly. To allow for maximal speed, both approaches were implemented in the low-level language Fortran 77... After carrying out the requisite algebra, and programming streamlined Gibbs sampling in R, we found that Markov chain Monte Carlo fitting... Lastly, we implemented streamlined Gibbs sampling using the low-level C++ language with the aid of the R packages Rcpp (Eddelbeuttel et al., 2020a), Rcpp Armadillo (Eddelbeuttel et al., 2020b) and Rcpp Dist (Duck-Mayr, 2018). |
| Open Datasets | Yes | The data are publicly available from the U.S. National Archives with identifier 606622. |
| Dataset Splits | No | The paper mentions simulated data where "the resident sample size within each town is 25" and for the real data "the number of infants followed longitudinally is 44,708 and the number of fields is 125,564". However, it does not specify any training/test/validation splits for these datasets. |
| Hardware Specification | Yes | The study was run on a Mac Book Air laptop with a 2.2 gigahertz processor and 8 gigabytes of random access memory. |
| Software Dependencies | Yes | The results for Markov chain Monte Carlo-based analysis using rstan (Stan Development Team, 2020), the R (R Core Team, 2020) interface to the Stan language, are also shown...Lastly, we implemented streamlined Gibbs sampling using the low-level C++ language with the aid of the R packages Rcpp (Eddelbeuttel et al., 2020a), Rcpp Armadillo (Eddelbeuttel et al., 2020b) and Rcpp Dist (Duck-Mayr, 2018). |
| Experiment Setup | Yes | The number of mean field iterations was fixed at 50... The number of mean field variational Bayes iterations is 100 and the Markov chain Monte Carlo results are based on a warmup sample of size 1,000 and a retained sample of size 1,000. |