In this thesis, several methods are proposed to construct sparse models in different situations with the special structures of group variable selection, partial correlation estimation and transcript regulation network construction. Traditional variable selection methods do not consider the special structures or cannot directly be applied to these situations. The methods proposed in this thesis are extensions and improvements of the Lasso method done by considering the special structures of different problems. These methods can be applied to high-dimensional data where the number of parameters are much larger than the number of observations. Simulation studies and real data analysis showed that these methods performed favorably, compared with some other recently developed models.
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