Computes the Gaussian variational approximation of the Bayesian 
    empirical likelihood posterior. This is an implementation of the function 
    found in Yu, W., & Bondell, H. D. (2023) <doi:10.1080/01621459.2023.2169701>.

The shared random effects joint model is one of the most widely used approaches to study the associations between longitudinal biomarkers and a survival outcome and make dynamic risk predictions using the longitudinally measured biomarkers. 
    One major limitation of joint models is that they could be computationally expensive for complex models where the number of the shared random effects is large.  
    This package can be used to fit complex multivariate joint models using our newly developed algorithm Jieqi Tu and Jiehuan Sun (2023) <doi:10.1002/sim.9619>, which is based on Gaussian variational approximate inference and is computationally efficient.

Fit and simulate latent position and cluster models for network data, using a fast Variational Bayes approximation developed in Salter-Townshend and Murphy (2013) <doi:10.1016/j.csda.2012.08.004>.

Contains functions for a variational Bayesian method for sparse PCA proposed by Ning (2020) <arXiv:2102.00305>. There are two algorithms: the PX-CAVI algorithm (if assuming the loadings matrix is jointly row-sparse) and the batch PX-CAVI algorithm (if without this assumption). The outputs of the main function, VBsparsePCA(), include the mean and covariance of the loadings matrix, the score functions, the variable selection results, and the estimated variance of the random noise.

Vector binary tree provides a new data structure, to
 make your data visiting and management more efficient. If the
 data has structured column names, it can read these names and
 factorize them through specific split pattern, then build the mappings
 within double list, vector binary tree, array and tensor mutually, through
 which the batched data processing is achievable easily. The methods of
 array and tensor are also applicable. Detailed methods are described in
 Chen Zhang et al. (2020) <doi:10.35566/isdsa2019c8>.