Essay on Network Estimation : Graphical Model
The following projects involve network estimation problems encountered in different biological appli- cations such as gene-gene or protein-protein interaction. The main focus has been on to develop robust, scalable network estimation methodology.
Quantile based graph estimation
Graphical models are ubiquitous tools to describe the interdependence between variables measured si- multaneously such as large-scale gene or protein expression data. Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices and they are generated under a multivariate normal joint distribution. However, they suffer from several shortcomings since they are based on Gaussian distribution assumptions. We have developed  a novel Bayesian quantile based approach for sparse estimation of graphs. The resulting graph estimation is robust to outliers and
applicable under general distributional assumptions. In the theoretical development, the graph estimation consistency result is also established. Along with standard MCMC, we have developed a fast posterior approximation technique based on variational method.
Nonlinear multivariate regression with latent graph
In this application, motivated by protein-protein residual interaction when modeled by covariates (RNA), multivariate regression is considered where the mean function is not necessarily linear. It is assumed that even after…