Interactive Lasso Model And Improved ADMM Algorithm

With the advent of the big data era, there are “dimension disaster” problems in many fields. In order to find out the useful information from large number of high-dimension datas, feature selection has become the first choice of many experts and scholars. However, traditional feature selection method rely on the original characteristics of high-dimensional data, and seldom consider interaction between the features. This paper based on the idea of feature interaction, put it into the regression model feature extraction and classification, and add the hierarchical constraint on the model in order to the main effects and interactive feature modeling. Then the penalty function is added into it. Its purpose is to contract coefficient of model, get the sparse solution of main effects and interaction coefficients, enhance stability and improve the efficiency of the model.First, we introduce weak hierarchical interaction logistic model, and propose neighbor operator algorithm based on the general iterative shrinkage and threshold optimization framework to solve the model. Then we use properties to simplify model algorithm and test in the simulated data and real data. The experimental results prove that the proposed approach has characteristics of interpretability, high classification performance and short run time.And then, this article consider task of fitting regression model, involving a collection of potential interaction between the covariate. During this period, we want to generate strong stratification. The author adopts a common framework, called a FAMILY. It can be turned into a solution of a convex optimization problem. For the strong hierarchical linear interaction lasso, this article use multiplier method of alternating direction algorithm to obtain model parameters. The algorithm guarantee converge to global optimum, and it can be easily specializes in any interested convex penalty function. And it can allow simply extension to the generalized linear model and the establishment of a high order model. The paper study on simulation data, ozone data and weather data to experiment. The results show that strong hierarchical generalized linear interaction can get better predict performance.Finally, The authors studied generalized strong hierarchical Interactive logistic regression. First, we define the generalized strong Hierarchical Interactive logistic model definition, and then give an improved ADMM solving method. Finally, using hepatitis experimental data and Parkinson’s data to experiment. Experimental results prove that the generalized strong hierarchical logistic method in handling interactive features data is superior to the Lasso, hierarchical Lasso.