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Activity Number: 163
Type: Topic Contributed
Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Computing
Abstract #311576 View Presentation
Title: Sparse Regression Incorporating Graphical Structure Among Predictors
Author(s): Guan Yu*+ and Yufeng Liu
Companies: University of North Carolina at Chapel Hill and University of North Carolina at Chapel Hill
Keywords: Prediction ; Model Selection ; Graph ; Sparse Regression ; Neighborhood ; Lasso
Abstract:

With the abundance of high dimensional data in various disciplines, sparse regularized techniques are very popular these days. In this paper, we use the structure information among predictors to improve sparse regression models. Typically, such structure information can be modeled by the connectivity of an undirected graph. Most existing methods use this graph edge-by-edge to encourage the regression coefficients of corresponding connected predictors to be similar. However, such methods may require expensive computation when the predictor graph has many edges. Furthermore, they do not directly utilize the neighborhood information. In this paper, we incorporate the graph information node-by-node instead of edge-by-edge. To that end, we decompose the true regression coefficient as the sum of some latent parts and incorporate group penalty functions to use predictor graph neighborhood structure information. Our proposed method is quite general and it includes adaptive Lasso, group Lasso and ridge regression as special cases. Both theoretical study and numerical study demonstrate the effectiveness of the proposed method for simultaneous estimation, prediction and model selection.


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