# Financial Data Quality Evaluation Method Based on Multiple Linear Regression
## 3 Construction of Quality Evaluation Model Based on Multiple Liner Regression
### Feature Selection Based on Shapley Value  
Feature selection and hyperparameter tuning are two important steps in every machine learning task. They help improve performance most of the time but have the disadvantage of being expensive in time. The more parameter combinations, or the more precise the selection process, the longer the duration. The usual approach is to combine tuning and feature selection. For feature selection, we adopt a ranking-based selection algorithm. Rank selection involves iteratively removing less important features while retraining the model until convergence is reached. SHAP helps when we perform feature selection using ranking-based algorithms. Instead of using the default variable importances generated by gradient boosting, we choose the best features, e.g., the one with the highest Shapley value.  
The Shapley value originates from cooperative game theory and is a distribution method based on contribution. It requires that profits and costs be fairly shared among each agent in an alliance [22]. The Shapley value has numerous applications in machine learning, including data pricing, federated learning, interpretability, reinforcement learning, and feature selection [23].  
The equation for the Shapley value of \(n\) members is as follows [24]:  
\[\phi_{i}(v)=\sum_{S\subset N,i\in S}\frac{(|S|-1)!(n-|S|)!}{n!}[v(S)-v(S-\{i\}) ],i=1,\ldots,n, \tag{4}\]  
where \(\frac{(|S|-1)!(n-|S|)!}{n!}\) represents the probability of member \(i\) joining the alliance \((|S|-i)\). The denominator represents the number of permutations of \(n\) members. The numerator represents the number of permutations of the first \((|S|-1)\) members entering the alliance \((|S|-i)\). Upon joining the alliance, member \(i\) acquires a certain value, denoted as \([v(S)-v(S-\{i\})]\). This value represents the contribution that member \(i\) makes to the alliance \(S\).  
In numerous scenarios involving data mining and machine learning, we frequently encounter challenges, such as the high dimensionality of features [25] and unknown relationships. In this study, we adopted the Powershap algorithm to select and eliminate indicators [26].  
The following steps outline the automated feature selection methodology implemented through Powershap, which is constructed based on the foundation of the genetic algorithm:  
1. Population initialization: A set of feature subsets is randomly produced, marking the formation of the initial population.
2. Fitness evaluation: A fitness function is implemented to assess the aptness of each entity, employing metrics like accuracy, F1 score, and so forth.
3. Selection process: Individuals exhibiting higher fitness are chosen to serve as the base for the next-generation population as determined by the fitness function assessment results.
4. Crossover procedure: Using a crossover operation, select individuals with superior fitness are randomly amalgamated to generate new offspring.
5. Mutation procedure: To enhance the population's diversity, random alterations are introduced to the new offspring through a mutation operation.
6. Iteration: Steps 2-5 are reiterated until the predetermined stop conditions are satisfied.