A Study On Feature Importance Of Complex Models Based On HDMR

As huge amounts of data have been generated and collected,machine learning is being widely used to build predictive models in many fields,such as image classification,user behavior prediction and credit score evaluation.Because of practical requirements,prediction accuracy is often the main or sole evaluation criterion for machine learning models.Generally,complex model is the guarantee to accuracy,and simple and interpretable models cannot be the most accurate predictors.Therefore,the pursuit of high accuracy results in that many machine learning models,such as neural network and random forest,are becoming so complex that they are not easy to understand.In practice,high prediction accuracy is often not enough.Data scientists and model users tend to gain insight into models.For example,doctors need to understand what physiological indicators in a model,such as blood pressure and diabetes,are crucial to predict the status of patients,which may be the key to find an efficient way to improve patients'health.A mortgage loan company is required by industry regulators to clarify what customer information are the main reasons to reject loan applications.Interpretation of prediction models has many benefits.First,it can help understand data and discover complex patterns by providing concise expression of data relationship.Second,it can increase trust of model builders and users by revealing the internal mechanism of models.Third,it can be used to diagnose and improve models by finding why a model fail to generalize.Most current methods of interpreting supervised learning models process by discovering the relationship between input features and predictions,and can be divided into three categories:(1)Discovering the impact patterns of input features on predictions by visualizing the changes of prediction as a function of input features.(2)Detecting feature interaction.(3)Measuring the contributions or importance of input features to prediction.This study focuses on measuring the feature importance of input features to prediction.Feature importance can be measured from either a global view,which measure feature importance for a whole data set,or a local view,which measure feature importance for a single instance.The main contents of this study are as follows:(1)Global feature importance:As the interpretability of complex machine learning models on biased data remains a difficult problem,it is crucial to provide a robust feature importance method of complex models for users.Therefore,this study proposes a novel method derived from high-dimensional model representation(HDMR)to measure feature importance.The proposed method can provide robust estimation when the input features follow contaminated distributions.Moreover,the method is model-agnostic,which can enhance its ability to compare different interpretations due to its generalizability.Experimental evaluations on artificial models and machine learning models show that the proposed method is more robust than the traditional method based on HDMR.(2)Local feature importance:Most local methods do not consider the correlation of input variables and the decomposition of feature importance.Therefore,this study proposes an agnostic method,based on high dimensional model representation(HDMR),to interpret supervised learning models by measuring local feature importance.The HDMR-based feature importance method is proven to be a unified framework with some good properties,which covers many other known methods.The HDMR-based feature importance can be decomposed into individual effects and combined effects.Moreover,some estimation methods for measuring local feature importance are proposed and summarized under different situations.Some experiments show the effects of individual feature and feature combination,and compare the performance of some approximate estimation methods.(3)Application research of feature importance methods:This paper applies the proposed feature importance methods in the model interpretation of a real data training model,calculates and discusses the results of global feature importance method and local feature importance method,respectively,and verifies the feasibility of the proposed methods in real application scenarios.The main contributions of this study are reflected in the following four aspects:(1)This study proposes a global feature importance method based on HDMR to interpret complex prediction models.The proposed method derived from HDMR yields an improvement in robustness compared to the traditional method based on HDMR when the input features follow contaminated distributions.And the proposed method is a novel global feature importance method that is model-agnostic.Moreover,due to its general applicability,the method can compare different interpretations among different artificial or machine learning models.(2)This study proposes a local feature importance method based on HDMR to interpret complex prediction models.The proposed method is defined by extending high dimensional model representation(HDMR)of the interpreted model.The HDMR-based method allows features'importance to be further decomposed into two parts:importance of individual feature and importance of feature combination.Through experimental analysis,we find that the importance of feature combination come from two sources:the feature interaction and the feature correlation.Moreover,several atomic characteristics and their related proofs of the HDMR-based method are exhibited.(3)Three kinds of estimation methods are summarized and put forward to calculate the local feature importance under different circumstances.And the second estimation method is proposed and categorized as pertaining to either feature independence or dependence.Moreover,the third estimation method is proposed to be suitable for tree-based models,such as random forest and Adaboost,and an efficient calculation formula and its related proof are given.(4)This study proposes a unified framework to compare different local importance methods.It is proved that the Shap measure is a special case of the HDMR-based method.The Shap measure has been proved to cover many local methods under certain conditions,including LIME,salience maps,DeepLift,LRP and Q?.