Fully Simplified Multivariate Normal Updates in Non-Conjugate Variational Message Passing

Authors: Matt P. Wand

JMLR 2014 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental We now provide illustrations of non-conjugate variational message passing that use Multivariate Normal updates. The first Illustration involves a Poisson mixed model and simulated data. We show, in detail, how Theorems 1 and 2 lead to a simple variational algorithm for such models. Figure 1 displays side-by-side boxplots of accuracy scores defined by accuracy(q ) = 100 1 1 q (θ) p(θ|y) dθ %. (11) for a generic parameter θ, and with p(θ|y) replaced by a kernel density estimate based on the MCMC sample. The boxplots show that the majority of accuracy scores exceed 95%, and that they rarely drop below 90%.
Researcher Affiliation Academia Matt P. Wand EMAIL School of Mathematical Sciences University of Technology, Sydney P.O. Box 123, Broadway NSW 2007, Australia
Pseudocode Yes Algorithm 1: Iterative scheme for determination of the optimal parameters in q (β, u), q (σ2) and q (a) for the posterior density function approximation (9).
Open Source Code No The text only mentions third-party software (Infer.NET computational framework, BRugs package, R computing environment) that the authors used, but does not provide their own implementation code for the methodology described in this paper. No explicit statement of the authors' code being released is found.
Open Datasets Yes This illustration involves analysis of data from the Californian air pollution study described in Breiman and Friedman (1985).
Dataset Splits No The paper mentions generating datasets or the total size of a dataset (e.g., "I replicated 1000 data-sets" and "The data comprises 345 measurements"), but it does not specify how these datasets are split into training, validation, or test sets for model evaluation.
Hardware Specification No No specific hardware details (like GPU/CPU models, memory, or cloud instances) are mentioned for running the experiments.
Software Dependencies Yes Note that, for general d, Dd can be obtained via the duplication.matrix() function in the package matrixcalc (Novomestky, 2008) within the R computing environment (R Development Core Team, 2013). For MCMC I used the package BRugs (Ligges et al., 2012) within the R computing environment (R Development Core Team, 2013).
Experiment Setup Yes The hyperparameters were set at σβ = A = 105 and the sample sizes were m = 100, n = 10. The iterations in Algorithm 1 were terminated when the relative change in log p(y; q) fell below 10 4. For MCMC I used the package BRugs (Ligges et al., 2012) within the R computing environment (R Development Core Team, 2013) with a burnin of size 5000 followed by the generation of 5000 samples, with a thinning factor of 5.