Unifying Variable Importance Scores from Different Machine Learning Models Using Simulated Annealing

Abstract

Each machine learning algorithm might generate different variable importance even though the identical loss function is used. The difference in the predictor rank order makes it difficult to interpret, so a single predictor rating is required. This paper proposes a method that combines predictor rating from machine learning using simulated annealing algorithms. Simulation and empirical data are used to apply the method and its evaluation. The simulation data contain as many as 24 predictors, 1000 observations, and 100 iterations. Four machine learning algorithms are used: random forest, XGBoost, neural network, and support vector machine. Then, four permutation importance variables were produced with 100 repetitions. Next, a simulated annealing algorithm generates a combined variable importance. This proposed method will be optimal if predictors are independent, and the number of predictors is more than ten. Then, the proposed method was applied to empirical data. Using the proposed method, the machine learning model needs only 14 predictors to reach the accuracy of 74.4% which is similar to the result if the algorithm involves all predictors. The proposed method is possible to be further developed and modified. The change could be employed in the objective value and the solution strategy within the simulated annealing procedure.