Application of new probabilistic graphical models in the genetic regulatory networks studies

This paper introduces two new probabilistic graphical models for reconstruction of genetic regulatory networks using DNA microarray data. One is an Independence Graph (IG) model with either a forward or a backward search algorithm and the other one is a Gaussian Network (GN) model with a novel greedy search method. The performances of both models were evaluated on four MAPK pathways in yeast and three simulated data sets. Generally, an IG model provides a sparse graph but a GN model produces a dense graph where more information about gene-gene interactions is preserved. Additionally, we found two key limitations in the prediction of genetic regulatory networks using DNA microarray data, the first is the sufficiency of sample size and the second is the complexity of network structures may not be captured without additional data at the protein level. Those limitations are present in all prediction methods which used only DNA microarray data.Comment: 38 pages, 3 figure

Partially linear additive quantile regression in ultra-high dimension

We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete picture of the conditional distribution of a response variable given high dimensional covariates. (2) The sparsity level is allowed to be different at different quantile levels. (3) The partially linear additive structure accommodates nonlinearity and circumvents the curse of dimensionality. (4) It is naturally robust to heavy-tailed distributions. In this paper, we approximate the nonlinear components using B-spline basis functions. We first study estimation under this model when the nonzero components are known in advance and the number of covariates in the linear part diverges. We then investigate a nonconvex penalized estimator for simultaneous variable selection and estimation. We derive its oracle property for a general class of nonconvex penalty functions in the presence of ultra-high dimensional covariates under relaxed conditions. To tackle the challenges of nonsmooth loss function, nonconvex penalty function and the presence of nonlinear components, we combine a recently developed convex-differencing method with modern empirical process techniques. Monte Carlo simulations and an application to a microarray study demonstrate the effectiveness of the proposed method. We also discuss how the method for a single quantile of interest can be extended to simultaneous variable selection and estimation at multiple quantiles.Comment: Published at http://dx.doi.org/10.1214/15-AOS1367 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org