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Book Summary:
New high-throughput technologies are generating many types of very high-dimensional genomic and proteomic data. These data can potentially be used for predicting clinical outcomes, for studying gene regulatory sub networks and for studying interindividual differences in responses to drugs. In practice, however, the number of independent samples is usually very small compared to genomic data's high-dimensional nature. As a result, many standard statistical methods cannot be applied directly or perform poorly in such high-dimension and low-sample size settings. In this dissertation, we propose to study several penalized estimation procedures for the following two problems: (1) To relate microarray gene expression data to censored survival outcomes. (2) To estimate the sparse precision or concentration matrix of the sparse Gaussian graphical model for inference of genetic networks. For the first problem, we investigate the use of L1 penalized estimation and threshold gradient methods for building predictive models and identifying genes related to patients' survival. We also propose a dimension-reduction procedure for the Cox model. Simulations and applications to real data sets indicate that the proposed procedures work well in predicting the time to event. In addition, relevant genes can be identified by the proposed procedures. For the second problem, we propose a threshold gradient descent regularization procedure for estimating the sparse Gaussian concentration models and demonstrate its application in generating genetic networks based on microarray gene expression data. By taking into account the sparsity of the networks, the proposed estimation procedure results in better estimates of the precision matrix and better inference of the genetic networks. Such a procedure is computationally feasible and can easily incorporate prior knowledge of the networks. |
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