Studies of the adaptive network-constrained linear regression and its application

The network-constrained criterion is one of the fundamental variable selection models for high-dimensional data with correlated features. It is distinguished from others in that it can select features and simultaneously encourage global smoothness of the coefficients over the network via penalizing the weighted sum of squares of the scaled difference of the coefficients between neighbor vertices. However, because more features were selected while it was applied for the process of analysis of the “China Stock Market Financial Database—Financial Ratios”, the so-called adaptive network-constrained criterion was proposed to tackle the problem via assigning various weights to the lasso penalty. Similar to the adaptive lasso, the proposed model enjoys consistency in variable selection if the weights have been given correctly in advance. The simulations show that the proposed model performed better than the other variable selection techniques mentioned in the paper with regards to model fitting; meanwhile, it selected fewer features than the network-constrained criterion. Furthermore, the mean value of the cross-validation likelihood and the number of selected features are tested to be accurate enough for practical applications.