Research Article
A Two-Stage Regularization Method for Variable Selection and Forecasting in High-Order Interaction Model
Inputs: the dataset | : maximum number of iterations used in the SRHR algorithm of the first stage; | : maximum number of iterations used in the SRHR algorithm of the second stage; | : the error tolerance used in the SRHR algorithm of the first stage; | : the error tolerance used in the SRHR algorithm of the second stage; | : scale parameter used in the SRHR algorithm of the first stage; | : scale parameter used in the SRHR algorithm of the second stage; | Output: The forecasting test error and selected pattern; | Randomly divide the original data into the training dataset and | test dataset . | The first stage using SRHR algorithm: | Generate grid values of and . | forto | forto | Initialization: , | Scaling: | while or do | Step 1. | Step 2. | Step 3. | Step 4: | end while | end for | end for | Obtain the solution path and the corresponding sparsity patterns based on | EBIC criterion. | The second stage using SRHR algorithm: | Generate the high-order interaction model and based | on the sparsity pattern . | Generate grid values of and . | forto | forto | Initialization: | Scaling: | while or do | Step 1. | Step 2. | Step 3. | Step 4: | end while | end for | end for | Obtain the solution path and update the sparsity patterns using | HDBIC criterion. | Calculate the test error using test dataset |
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