A Factor Marginal Effect Analysis Approach and Its Application in E-Commerce Search System

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Introduction
Feature explanation has attracted increasing attention in both industry and academic communities.It can not only enhance users' trust in the e-commerce search system but also help them make better and faster decisions.Murdoch et al. [1] discuss the defnition of interpretability and how to select and evaluate the machine-learning models for interpreting.Guidotti et al. [2] summarize and classify the methods for interpreting black-box models in machine learning.Kohavi et al. [3] share how to develop experiment platforms to make it harder for experimenters to be misled, which is used to explain the intuition through solid statistical reasoning.Scott [4] introduces the core idea of the SHAP algorithm in game theory and how to apply it in feature interpretation.Shrikumar et al. [5] study how to calculate feature importance from SHAP perspective in game theory.Bai et al. [6] introduce attentional mechanism that applies in explainability.Chang et al. [7] studied the interpretability of generalized linear models.Explainable machine learning techniques [8] are employed to quantify the contributions of the impacting factors to the time efciency, thereby identifying the fundamental causes.In [9][10][11], the interpretability of neural networks is studied.Qi et al. [12] introduce the interpretability of adversarial training.Ge et al. [13] propose an explainable fairness framework, which can discover critical features and calculate an explainability score for fairness.LiEGe (listwise explanation generator) [14] studies the problem of content-based explanation of search results in the two newly defned settings: novelty and comprehensive explanation generation.Rossi et al. [15] propose an explainability framework for embedding-based link prediction, which can be applied to any embeddingbased LP model.In [16], session-based recommendation with interpretability, which is guided by meta-path and self-attention mechanism, is studied.Reference [13] is an interpretable research based on recommendation fairness.Nizri et al. [17] propose an automatic method that generates intuitive explanations for a SHAP-based payof allocation, which provides customized explanations for SHAP values.Balog and Radlinski [18] propose evaluating explanations for item recommendations, which presents an analysis of intentions behind explanations.Tsukuda and Goto [19] propose an explainable recommendation method for repeat consumption, which designs nine explanation styles and validates the persuasiveness of these styles.A feature refnement network [20] is proposed, which learns context-aware feature representations at bit level to explain features in diferent contexts.Kunkel et al. [21] analyze both direct and indirect efects among constructs of major interest for RS research, which includes explanation quality, recommendation quality, social presence, and trustworthiness.
Despite efectiveness, these explainable recommender models still sufer from some limitations.It is difcult for these existing methods to provide quantitative deterministic guidance, such as how much one-dimensional feature can be improved and how much recommendation trafc can be improved.Further analysis is needed in conjunction with the data.Inspired by these limitations, we proposed a novel explainable feature quant algorithm based on game theory.
To summarize, our major contributions are listed as follows: (1) To the best of our knowledge, this is the frst work that demonstrates the efectiveness of applying the explainable feature marginal contribution approach, which uses features of the shop owner's concern for search system factor quantization.(2) Te FMEA can compute how much one-dimensional feature contributes to the enhancement of online trafc, which is used to efectively guide merchant operations.(3) We design a second-order interpolation operator, which is used to transform the game theory SHAP value into the product cross probability.In this way, it can learn business interpretation better.(4) Te case study can help the operator explain online bad cases and give reasonable diagnostic suggestions.
(5) We verifed the efectiveness of the algorithm in Large-Internet-Company data, which brings a revenue increase of +10.05% for the fow index, +7.54% for the user feedback, and +2.46% for the service index.(6) Our solution fts product rankings with explainable features, which map trafc scores to multiple dimensions.In this way, merchants can easily understand the position of a product in the industry and diagnose their problems.Te purpose is to provide business operation suggestions, model the impact of operation intensity on factor changes, and guide trafc improvement.
Te remainder of this paper is organized as follows.Section 2 provides a synopsis of related works.Te preliminaries of our work are provided in Section 3. Te framework concept and the proposed factor marginal efect analysis (FMEA) approach are introduced in Section 4. Te dataset and experimental result analysis are thoroughly examined in Section 5. Finally, Section 6 contains an overview of the previous sections as well as some discussions in future work.

Related Work
In the era of big data, feature explanation [22] plays an important role in increasing product sales and assisting human decision-making.Interpreted modeling clearly tells businesses which factors have more infuence on search trafc, so as to provide business diagnosis and guidance.Studies have shown that providing appropriate explanations [23] could improve user acceptance of the recommended items, as well as beneft user experience in various other aspects, including system transparency [24], user trust, effectiveness, efciency, and satisfaction.
2.1.Feature Importance.Feature importance is a key tool for interpreting the constructed models and analyzing the relationship between features and labels.We defne feature importance [25,26] as any quantitative assignment of infuence to the features used by machine-learning models.On the one hand, feature importance techniques attribute importance to a feature in relation to the model or its predictions.On the other hand, feature importance techniques produce explanations related to the business.Shapley value [4,5,27] is the weighted sum of a feature's contribution to the total prediction over all possible feature combinations.Tis method approximates the Shapley value of each layer in the deep neural model and then calculates the contribution of features.Permutation feature importance [28] measures the signifcance by rearranging the features randomly on the dataset and then evaluating the rate of change in loss.TAYLOR expansion [29] is used to obtain the smooth derivative of the nonlinear loss function.Te relevant method calculates the variance of the neuron weight change during the training process, which is employed to measure the feature importance.

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International Journal of Intelligent Systems 2.2.Feature Explanation.Te idea of interpretable machine learning [30] is to consider both the prediction accuracy and model interpretability and try to fnd the best balance between them.Based on diferent scenarios, the interpretability can be divided into intrinsic interpretability and ex post interpretability.An attentive recurrent neural network (Ante-RNN) [31] for the dynamic explainable recommendation is proposed, which can provide multimodel explanations according to the user dynamic features.

Intrinsic Interpretability.
Intrinsic interpretability means that the structure of the model is relatively simple and the user can clearly see the internal structure of the model.Te model has an interpretable efect at design time.Traditional statistical models (such as linear regression [32], logistic regression [33], and decision trees [34]) have strong interpretability.However, these models are less accurate.An explainable medical recommender system uses graph concepts to provide an interpretable approach [35] to medical data, which is based on community detection algorithms.Explainable boosted linear regression (EBLR) [36] for time series forecasting is proposed, which is an iterative method that starts with a base model, and explains the model's errors through regression trees.

Ex Post Interpretability.
Ex-post explainable [37] methods can better enhance the interpretability of a model and extract valuable information after training.Te popular deep learning has complex internal structures.It is difcult to observe the changes of data neuron by neuron, and research on explainable machine learning has generated an enthusiastic response in both academia and industry.A novel method to explain black-box models [38] is proposed, which employs numeric association rules to explain and interpret multistep time series forecasting models.A new deep learning architecture xDNN [39] is proposed, which combines reasoning and learning in a synergy and explains its efciency in terms of time and computational resources.

Preliminaries
In this section, we frst formally defne the problem and then provide several key notions relevant to our proposed solution.Te motivation of this research is also provided.

Problem Defnition.
To improve efciency, the existing ranking model in e-commerce search systems is complex, leading to a lack of understanding of trafc distribution strategies.Te interpretable model can help us gain a deeper understanding of trafc distribution strategies and provide guidance and suggestions.Our solution enhances the explainability of business factors, with the goal of covering all factors.Te explainable approach makes the subsequent estimation of operational efects more comprehensive and accurate.Compared with feature importance, the biggest advantage of SHAP value is that it can refect the infuence of each feature in each sample and also exhibit a positive or negative impact.Terefore, we choose to design our solution based on the SHAP value.For each sample, the model produces a predicted value, and the SHAP value is assigned to each feature of the sample.Te target formula is as follows: y i represents the predicted value for the i-th sample, y b ase describes the baseline of the model, f(x i,j ) shows the contribution of the j-th feature of the i-th sample to the predicted value, and k represents the number of features.
Based on the calculated SHAP values, we verify the distribution of interpretable factors.Our defnition of interpretability in this study is as follows: if product A ranks higher than product B, there must be at least one factor whose SHAP value in product A is greater than that in product B.

Key Notions.
Here, we discuss the necessary notions of our framework.Click-through rate (CTR): in the e-commerce feld, search ranking models estimate the click-through rate of users and then combine other business considerations to determine product ranking.Our interpretability method can be used to explain the marginal contribution of diferent factors to the target variable.
SHAP: Shapley value is mainly used to solve the allocation equilibrium problem in cooperative game theory [40].Tis study focuses on the e-commerce search system, and frst uses actual features to model the product ranking, and then introduces SHAP to explain the model.Te SHAP value can not only explain the importance of features but can also quantify and estimate the positive or negative impact on label variables.Compared with other feature explaiable methods, information gain can intuitively refect the importance of each feature for the model's predictive value, but cannot quantify the positive and negative relationship between features and the fnal results.Terefore, our interpretable solution chooses the SHAP value.

Research Motivation.
Te existing ranking model of the e-commerce search system has a complex structure and a large capacity, resulting in a lack of understanding of trafc distribution strategies.At the same time, businesses do not understand the rules of search ordering and lack an operational grasp in marketing linkage.To better solve these problems, we propose an explainable scheme, which uses the factors that have an impact on the target, and then analyzes the relationship between the trafc distribution factor and the commodity ranking.Compared with other baselines, the advantage of our approach is that it can refect the infuence of the features in each sample and also show the positive and negative infuence.
International Journal of Intelligent Systems

Our Method
Tis section introduces our proposed framework, named explainable factor marginal efect analysis (FMEA) approach based on game theory.Te FMEA framework consists of two stages that are applied recursively: predict model training and feature explanation.Te frst stage utilizes well-known machine learning or deep learning models.Te second stage generates features' marginal efect based on game theory.Our explainable model architecture is shown in Figure 1.

4.1.
Search System Feature Explanation Scenario.Te Large-Internet-Company's search system feature explanation aims at stimulating the commodities trafc that reaches the linkage threshold after shop owners paid marketing.Feature explanation brings two main efects.First, more active advertising brings more revenue to Large-Internet-Company. Second, it helps shop owners manage the search and recommendation trafc better and brings a positive impact for their sales.To promote shop owner's awareness of linkage efect and facilitate the business departments to control the delivery, we represent the impact of marketing linkage as an index that can be intuitively understood by the business.Based on game theory, the features' marginal contribution is mined and the deterministic infuence of marketing linkage factors is quantifed.
Te merchant does not know about the search rules for their goods.Tey lack the interpretative and instructive search operation tools, which often leads to malpractices such as fraudulent billing.Our interpretable approach uses the form of factor marginal contribution evaluation to help merchant clearly understand the overall level of their products in search and understand how to operate to improve their product rankings.In this scenario, the diagnosis process for businesses is shown in Figure 2.

Explainability of Feature Importance.
Te ex post explanation has attracted more and more attention in the industry.For better business interpretation, we map the SHAP value to real business probabilities as shown in Figure 3.

Feature Importance Based on the Game Teory.
Te feature set of training data is (feat 1 , feat 2 , . . ., feat n ), and the calculation formula of the marginal contribution of feature i is as follows: Formula ( 2) is an expected value, which represents the variation of x i prediction results between the participating model and the nonparticipating model under diferent feature combinations.M represents the complete set of features, and S represents the feature subset excluding x i .Te value of S has various conditions, which correspond to diferent feature combinations.Te formula is derived as follows: Step 1: extract x i from the feature set M with a probability of p.
Step 2: select a subset S from the remaining feature subset with a probability as follows: 1 Step 3: multiply the probabilities of step 1 and step 2.
Te product is the probability of each combination of features.
We propose a second-order interpolation operator as follows: Specifcally, the interpolation operator transformation is as follows: Te process of approximate Shapley estimation for a single feature importance is shown in Algorithm 1.

Feature Importance Based on Causal Inference.
First, regression solves the problem of optimal linear prediction.Let β * be a parameter vector: Linear regression fnds the parameter that minimizes the mean square error, and the linear solution is given by the following equation: We can estimate the beta by using the following formula: In data analysis, we want to estimate the causal efect of the variable T on the outcome of y.International Journal of Intelligent Systems variables and do not afect the calculation of this causal efect.For a regression variable T, the parameters associated with it are given by the following formula: where T is randomly assigned and β is the average causal efect.We have multiple regressors, which can extend the following formula to ft.We are really interested in estimating the parameters associated with T, and the other variables are auxiliary variables.
where τ can be obtained by the following formula: where  T l is the residual of all other covariates X 1i + • • • + X ki regression on T i .Tis means multiple regression coefcients are bivariate coefcients of the same regressors after considering the efects of other variables in the model.τ is the bivariate coefcient of T after all the other variables have been used for the prediction.Extending to the multivariable case, we see how regression provides a marginal explanation for the intervention factors after excluding other infuences.Te estimated value of the intervention factor coefcient can be interpreted as how the outcome changes with the intervention, holding all other included variables constant.
On the basis of factor explanation, we try to introduce the method of causality analysis, which calculates the feature importance by factor regression coefcient.Te results of feature importance are in agreement with the explainable theory, which further strengthens the confdence of our proposed method.

Feature Importance Merge.
We combine the feature importance of game theory and the causal inference, and the integrated feature importance is shown in Figure 4(a).To reduce the blank space in Figure 4(a), we divided the features into two groups.Features with similar value ranges were placed in the same group.We then drew two subplots using diferent coordinate scales, which are shown in Figure 4(b).
Samples and features of the recommended business continue to grow as the iterations and the number of model parameters also increase, but interpretability becomes important and difcult.In the actual scenario, especially in business operation diagnosis, it is necessary to give the business a certain degree of explanation, to help the business growth.At the same time, through intuitive explanation, it can improve the model efect and iteration efciency.

Explanation of the Feature Marginal Efect.
We improved the game theory model to calculate the marginal efects of diferent features, which are shown in Figures 5 and 6.
In Figure 5, the horizontal axis is the SHAP value, which represents the feature marginal contribution.Te vertical axis represents diferent features: the more red the color, the larger the feature value; the more blue the color, the smaller the feature value.Figure 6 is the result of mapping the SHAP value via the business operator.Te horizontal axis represents the probability of ranking improvement, which has more business signifcance compared to the SHAP value.Te vertical axis represents diferent features: the more red the color, the larger the feature value; the more blue the color, the smaller the feature value.
From Figures 5 and 6, the data performance of the main interpretable factors is as follows: queryFlowscore has a positive efect; the higher the queryFlowscore, the greater the rank probability upgrading.competeScore has a negative efect; the lower the competeScore, the greater the rank probability upgrading.When the queryTopRatio is at a low or high value, it is easier to achieve a higher rank probability upgrading.Te marketing output of the product has a positive efect, the higher the marketing output, the greater (1) Input: dataset with features and labels, pretrain model (2) Output: Shapley value for the value of the j − th feature (3) Required: number of iterations M, instance of interest x, feature index j, data matrix X, and machine learning model f (4) For all m � 1, . . ., M: (5) Draw random instance z from the data matrix X (6) Choose a random permutation o of the feature values (7) Order instance x: x o � (x (1) , . . ., x (j) , . . ., x (p) ) (8) Order instance z: z o � (z (1) , . . ., z (j) , . . ., z (p) ) (9) Construct two new instances, (10) With j: (11) x (+j) � (x (1) , . . ., x (j− 1) , x (j) , z (j+1) , . . ., z (p) ) (12) Without j: (13) x (− j) � (x (1) , . . ., x (j− 1) , x (j) , z (j+1) , . . ., z (p) ) (14) Compute marginal contribution: Compute the Shapley value as the average:   International Journal of Intelligent Systems the probability of achieving rank upgrading.Te conversion rate (CVR) performance of the product has a positive efect; the better the CVR performance, the greater the probability of achieving rank upgrading.Te click-through rate (CTR) performance of the product has a efect; the better the CTR performance, the greater the probability of achieving rank upgrading.Te gross merchandise volume (GMV) performance of the product has a positive relationship; the better the GMV performance, the greater the probability of achieving rank upgrading.Te better the order line performance, the greater the probability of achieving rank upgrading.

Online Deployment.
With the search ranking iterates, samples and features increasing, interpretability becomes more difcult.However, in the business, especially in the diagnosis of merchant operation for business, certain interpretability should be provided to merchants to help them grow.Besides, the explainability can also improve the customer experience of E-commerce platforms.In this article, we discuss the efect of interpretability for business.Te application of our explainability approach is shown in Figure 7.
Te online board includes priority id, diagnostic analysis, and quantifed guidance suggestions, which are shown in Table 1.

Datasets.
Our data come from the real scene of a Large-Internet-Company marketing linkage project.Tere are 31 features in total, including commodity features and marketing features.label is designed to increase the ranking of goods to 1 and decrease the ranking to 0. Te model training data volume distribution is shown in Table 2. Te main features used for training are shown in Table 3.We describe the details of the features from the following four dimensions: feature name, feature defnition, feature infuence mode, and feature business meaning.(1) Feature name: queryCompeteScore.Feature defnition: the competition degree of the main search terms placed on the product.Feature infuence mode: negative efect; that is, the lower the competition degree of search terms, the greater the probability of obtaining cross-ranking promotion.Feature business meaning: the degree of competition represents the proportion of products marketed under the word, that is, whether the product marketing is in a more competitive marketing environment.Te product is more afected by the marketing linkage, the query words of which have high degree competition.It is easier to show marketing efects under search terms with low competition.(2) Feature name: srOrderline7davg.Feature defnition: the order line performance of the product in the competitive product set.Feature infuence mode: positive relationship; that is, the better the order line performance, the greater the probability of obtaining cross-ranking promotion.Feature business meaning: compared with competing products, goods with more order lines are easier to obtain marketing linkage, and the positive relationship shown is consistent with cognition.
(3) Feature name: srCvr7davg.Feature defnition: cvr denotes the conversion rate of the product in the competing products.Feature infuence mode: positive efect; that is, the better the cvr performance, the greater the probability of obtaining cross-ranking promotion.Feature business meaning: the cvr of a product is closely related to the search core index, and compared with competing products, the product with good cvr is easier to obtain marketing linkage.(4) Feature name: srCtr7davg.Feature defnition: cTR denotes the click-through rate performance of the product in the competitive product set.Feature infuence  International Journal of Intelligent Systems mode: positive efect; that is, the better the cTR is, the greater the probability of obtaining cross-ranking promotion.Features business meaning: the cTR of a product is closely related to the search core indicators.Compared with competing sets, the product with good CTR performance is easier to obtain marketing linkage.( 5) Feature name: queryTo-pRatio.Feature defnition: the exposure ratio of the product on the head search term.Feature infuence mode: when the feature value is at a low value or an extremely high value, it is easier to obtain a higher probability of crossover lift.Feature business meaning: goods need to have a main source of fow, the head or tail query words of which are easier to get marketing linkage fow.( 6) Feature name: srGmv7davg.Feature defnition: GMV stands for the gross merchandise volume of the product in the collection of competing sets.Feature infuence mode: positive relationship; that is, the better the GMV is, the greater the probability of achieving cross-ranking promotion.Feature business meaning: compared with the competing sets, the products with high GMV are easier to obtain marketing linkage.( 7) Feature name: output.Feature defnition: marketing output of the product.Feature infuence mode: positive efect; that is, the higher the output is, the greater the probability of obtaining crossranking promotion.Feature business meaning: the output of marketing represents the inspection results of commodity quality through advertising, and it is easier to obtain marketing linkage for products with a good transformation efect.(8) Feature name: queryFlowScore.Feature defnition: the liquidity of the main search terms of the product.Feature infuence mode: positive efect; that is, the higher the fuidity of search terms for product placement, the greater the probability of obtaining cross-ranking promotion.Feature business meaning: liquidity indicates the degree of commodity rotation under the word, that is, whether there are more strong commodities under the word.Search terms with high liquidity have large space for increasing exposure and easily to get linkage improvement.

Ofine Evaluation.
We use AUC as ofine evaluation, and use as online evaluation.Te AUC (area under ROC curve) shows the ranking ability of the model; the higher the AUC, the better the model performance.It is defned as follows: where D+ is the set of positive examples, D− is the set of negative examples, g(.) is the value of model prediction, and I(.) is the indicator function.In the Large-Internet-Company dataset, the AUC of the baseline is 0.6918, the AUC of the DNN explainability is 0.7025, and the AUC of our method is 0.7134.

Online Evaluation.
Our online evaluation includes fow performance score, user feedback score, and service performance score.Te details are shown in Table 4.

Baselines
(i) Data analysis [41]: in industry, computing feature importance via data analysis decision-making can help e-commerce provide more efcient and accurate information services (ii) XGBoost [42]: tree boosting is a widely used machine learning method, which can compute feature importance via information gain of split nodes (iii) Permutation [43]: permutation feature importance can be combined with any regressors and classifers, which is widely used in deep neural networks.
Te disadvantage of data analysis is that it requires a lot of manual statistics, the analysis perspective depends on business experience, and manual experience is relatively limited.Te disadvantage of XGBoost and Permutation is that only feature importance can be calculated, but the marginal efect of each feature change on the target variable cannot be quantifed.Our proposed method solves the pain points of the abovementioned three bases and can automatically calculate the marginal efect of each feature.

Experimental Setup.
We implement all the models using Python 3.6.7 on GPU Tesla P40.To be fair, we divide the datasets into train data with 80%, valid data with 10%, and test data with 10%, and all of these models share the same train-valid-test datasets.We repeat each experiment 10 times and take the average value as the evaluation index.In all the experiments, we also use the same input features of items and users, as well as the other training hyperparameters.All comparison experiments use the sigmoid activation function and Adam optimizer, and the learning rate is 0.01.Besides this, the batch size is 1024, the epoch is 20, and regularity coefcient is used.

Explainable Efect Analysis.
Based on the whole category of Large-Internet-Company items, we analyze the linkage efect among conversion rate, query competition, and ranking uplift probability, which are shown in Tables 5 and 6.
Item conversion rate is closely related to the core index of search.Compared with similar products, the item with good performance of cvr is easier to obtain marketing linkage.As can be seen from Table 5, the better the conversion rate performance, the greater the probability of achieving uplift-grade promotion.
Competitive score represents the marketing linkage effect under the query words, which means competition degree of the product.Te search terms with high competition, the products are greatly afected by the linkage.Less competitive search terms are easier to refect linkage efects.As can be seen from Table 6, the lower the competition of search terms for product placement, the greater the probability of achieving cross-uplift promotion.

Case Study.
Our online business application scenario is to establish an interpretable and diagnosable trafc tool for merchants, providing operational leverage for merchants.10 International Journal of Intelligent Systems Te bad case performance can be explained by using the factor marginal efect analysis method (FMEA).In the "personal care" category, we found that the marketing input of "product id � 100027183286" exceeded 77% of the products in the same category, but the increase in ranking was only 8%.Te details are shown in Table 7.
In Table 7, compete denotes search word competition, output means item marketing output, and fuidity is search word competition.Terefore, our suggestion is to select search terms with low competition and good fuidity, so as to increase the linkage efect of the product in the search feld.
For the bad case in Figure 8, our proposed model is utilized to explain why it is difcult for the product to achieve rank upgrading.From the data analysis, we can see that four factors (competeScore, srCtr7davg, queryTopRatio, and product marketing output) have a signifcant impact on whether the product can achieve rank upgrading.Te competeScore factor has a signifcant negative efect (− 0.11) on the probability of rank upgrading for this product, and queryCompeteScore is higher than the overall situation of the category it belongs to, indicating that there are more competing products for the search term exposure of this product, making it difcult to achieve rank upgrading.Te srCtr7davg factor has a signifcant negative efect (− 0.08) on the probability of rank upgrading for this product, and the CTR is only higher than that of 13.7% similar products, lower than the overall situation of the category it belongs to, indicating that the conversion rate of the product is poor, making it difcult to achieve a ranking improvement in the search feld.Te queryTopRatio factor has a signifcant negative efect (− 0.06) on the probability of cross-rank upgrading for the product, and the queryTopRatio is higher than the overall situation of the category it belongs to, indicating that the product trafc mainly comes from the head search terms, making it difcult to achieve rank upgrading.Te product marketing output factor has a signifcant positive efect (+0.05) on the probability of rank upgrading for the product, and the marketing output is higher than the overall situation of the category, indicating that the product has more marketing investment on and of the platform, thereby increasing the probability of rank upgrading.Terefore, it is suggested to operate the search terms of this marketing product and choose low-competitive, waist-to-tail search terms for advertising, so as to increase the linkage efect of the marketing product in the search feld.

Data Analysis of the Regression Test.
In terms of the model's usability, we conducted validation from two perspectives: model accuracy and trend consistency to ensure that the model can not only predict the probability of rank upgrading of products accurately but also obtain insightful guidance to improve the product's rank probability.Figure 9 shows the validation of model accuracy, from which it can be seen that the prediction error of the model under each feature to the sample's actual performance is around 1%.     International Journal of Intelligent Systems Over a relatively long time period, the indicators are monitored and the collections of products with increased indicators and the collections of products with decreased indicators are compared.Figure 10 shows that the crossrank upgrading probability of the product collection has the same trend of change as the prediction.

Conclusion
We propose a factor marginal efect analysis approach (FMEA), which is used to quantize the correlation between online trafc and features.Specifcally, based on game theory, the FMEA can compute how much one-dimensional feature brings about the enhancement of online trafc.Besides, we design the high-order operator to quantify the feature contribution.Extensive experiments are conducted and the results demonstrate the efectiveness of our method.
In fact, the FMEA has been deployed in Large-Internet-Company search systems and successfully serving over hundreds of millions of consumers for online e-commerce service.Tis is the frst work to integrate game theory interpretability into machine learning to evaluate feature contribution, and more related studies will be further explored.
Tis study focuses on improving the machine learning explanation by considering the factor marginal efect analysis, which provides a novel explainable intelligent method.However, the limitation of our proposed method is that the precision of explainable causal intervention efects needs to be further addressed.Explainability may inspire the development of novel training methods and evaluation metrics that guarantee the trustworthiness and consistency of even the most complicated models.
In the future, our work can be further studied from both trafc diagnosis and factor prediction of return on

Figure 7 :
Scheme: Improving shap based on game theory

Figure 8 :
Figure 8: Te business sample of a bad case.

Figure 9 :
Figure 9: Te accuracy of model prediction vs truth label.

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Terefore, we use regression with this variable to estimate the efect.Even if we add other variables to the model, they are usually auxiliary

Table 1 :
Online board table.

Table 3 :
Description of feature engineering.

Table 4 :
Our method's improvement vs baseline.

Table 7 :
Performance of a bad-case analysis.
Figure 10: Predictive trend distribution for diferent feature intervals.International Journal of Intelligent Systems investment (ROI).Based on the improvement of game theory, trafc diagnosis can introduce a SHAP scheme with sample weighting to quantitatively estimate the contribution of each feature gap to the target variable.Trough the introduction of a causal inference algorithm, it can predict the ROI efect of business action space and provide suggestions.