Network Estimation : Graphical Model

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3 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
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Stochastic approximation (SA) provides a fast recursive way for numerically maximizing a function under measurement error. Using suitably chosen weight/step-size the stochastic approximation algorithm converges to the true solution, which can be adapted to estimate the components of the mixing distribution from a mixture, in the form of recursively learning, predictive recursion method. The convergence depends on a martingale construction and convergence of related series and heavily depends on the independence. The general algorithm may not hold if dependence is present. We have proposed a novel martingale decomposition to address the case of dependent data.
5 Measurement error model: small area estimation
We proposed [4] a novel shrinkage type estimator and derived the optimum value of the shrinkage pa- rameter. The asymptotic value of the shrinkage coefficient depends on the Wasserstein metric between standardized distribution of the observed variable and the variable of interest. In the process, we also estab- lished the necessary and sufficient conditions for a recent conjecture about the shrinkage coefficient to hold. The biggest advantage of the proposed approach is that it is completely distribution free. This makes the estimators extremely robust and I also showed that the estimator continues to perform well with respect to the ‘best’ estimator derived

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