## 3 Proposed Method  
The proposed methodology involves three stages. First, we investigate variables to identify those with high potential to form influential modules. Secondly, we generate highly influential variable modules from variables selected in the first stage, where variables of the same module interact with each other to produce a strong effect on \(Y\). Lastly, we combine the variable modules to perform the prediction process.  
From prior simulation experience, we demonstrated that the two basic tools, the I-score and backward dropping algorithm, can extract influential variables from data sets with regard to modules and interaction effect. However, questions remain on how to determine the input to the backward dropping algorithm and how to use the output from the algorithm results to construct prediction estimates. Unless we can appropriately use the input to and output from the backward dropping algorithm, the strength of the algorithm cannot be fully used. In this sense, the innovation of the proposed method manifests in three ways. First, if we directly apply the backward dropping algorithm on high-dimensional data sets, we may miss some useful information. We propose a two-stage feature selection procedure: interaction-based variable screening (this is called the interaction-based convolutional layer, see Section 3.3) and variable module generation via the backward dropping algorithm (which is called the interaction-based feature engineer, see Section 3.4). Since the impurity of features is largely enhanced by the interaction-based variable selection algorithm in the first stage, we were able to construct variable modules that have higher-order interactions with large amounts of information in the second stage. These variable modules provide support as building blocks for us to form classification rules. These schools of thoughts produce results significantly better than directly applying the backward dropping algorithm.  
The statistics, the influence score (I-score), works better with discrete variables. If some explanatory variables are continuous, we first convert them into discrete ones for feature selection purpose. After we have selected the important variables, we use the original values to estimate their effects. We rely on the influence score when we convert continuous variables into discrete variables. For example, if a random variable is drawn from normal distribution, then one optimal cutoff is to use the one that has the largest marginal I-score. There is a trade-off induced from this process: the information loss due to discretizing variables from continuous to discrete forms versus the information gain from robust detection of interactions by discretization. [PERSON] et al. [27] demonstrated that the gain from robust detection of interactions is much more than enough to offset possible information loss due to discretization. [PERSON] et al. [27] used the two-mean clustering algorithm to convert the gene expression level into a variable with two categories: high and low. As an additional piece of evidence supporting the proposed preprocessing step, the authors tried more than two categories, i.e., three categories of high, medium, and low. The empirical results showed that the more the categories used, the worse the classification error rates.