Nowadays a large amount of data is available, and the need for novel statistical strategies to analyze such data sets is pressing. This talk focuses on the development of statistical and computational strategies for a sparse regression model in the presence of mixed signals. The existing estimation methods have often ignored contributions from weak signals. However, in reality, many predictors altogether provide useful information for prediction, although the amount of such useful information in a single predictor might be modest. The search for such signals, sometimes called networks or pathways, is for instance an important topic for those working on personalized medicine. We discuss a new “post selection shrinkage estimation strategy” that takes into account the joint impact of both strong and weak signals to improve the prediction accuracy, and opens pathways for further research in such scenarios.