Methods Assessment for Interpretable Machine

Abstract

In this study, we introduce a generic experimental framework for measuring the degree of attribution methodologies generality and precision in terms of machine learning interpretability. In addition, we detail a way for gauging the consistency of two attribution approaches. In our experimental work, we concentrate on two well-known model-independent attribution techniques, namely SHAP and LIME, and evaluate them using two applications in the attack detection sector. Our introduced methodology demonstrates the lack of precision, generality, and consistency in both LIME and SHAP. As a result, attribution research needs to be examined more carefully.

Keywords

• 1 Artificial Intelligence
• Feature Attribution Methods
• Machine Learning Interpretability

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1. Introduction

Machine learning models are commonly used for solving different types of problems. From “simple” movie recommendation systems and personal voice assistants, to more “sensitive” domains that involve taking “high” impact decisions, such as mortgage approval models and healthcare decision support systems. Therefore, it became inevitable to democratize Artificial Intelligence (A.I.) in our society [1]. Regardless of the adoption expansion of ML models, the logic and mechanisms behind these models is still unknown to end users and experts, i.e. making these models be considered black boxes [2]. Therefore, depending on these ML algorithms for decision-making tasks that are sophisticated such as in aircraft collision detection systems without well understanding these models can lead to serious consequences [ 3 ]. Hence, in order to solve this problem, many interpretable models and explanation methods [2] have been proposed.

Being social impact of ML algorithms significantly increasing, the need for understanding the mechanism behind the decision-making process is also increasing along with it [ 4 ]-[ 7 ].

A big number of studies targeting this problem has been done. Specifically, Explainable Artificial Intelligence (X.A.I.) i.e. a field of study aiming at interpretable ML models development in order to make a transition to transparent A.I. [2], i.e. producing more explainable models and methods that explain existing black box models without compromising their predictive performance. Defense Advanced Research Projects Agency (DARPA) is a remarkable initiative in this research field, funded by the U.S. Department of Defense, which created the X.A.I. program for funding academic and military research [ 8 ]. Likely, “Preparing for the Future of Artificial Intelligence”- is a report published by the White House Office of Science and Technology Policy (OSTP) which represents another example of governmental initiatives emphasizing that A.I. systems should be open, transparent, and understandable for interrogating the assumptions behind the models decisions [ 9 ]. Many countries outside of the U.S.A. have already taken the initiative towards transparent A.I. . i.e., the French Strategy for Artificial Intelligence, The United Kingdom’s Academy of Sciences, and Portugal government, have published their roadmap towards interpretable A.I. [ 10 ]-[ 12 ]. The European Union announced that “A.I. systems should be developed in a manner which allows humans to understand (the basis of) their actions” in order to increase transparency and minimize the risk of bias error [ 13 ].

Interpretable A.I. practices in various A.I.-related fields have already became common in the Tech industry. Additionally, numerous companies are interested in interpretability in order to commercialize interpretable A.I. products as investments in this field. Google is promoting interpretability by including as a core part of their user experience the interpretability planning and treating, designing interpretable models, understanding and communicating their trained models explanations to the users [ 14 ]. FICO, is a credit score company that also addressed interpretability in credit scoring systems [ 15 ] as it has published a white paper with the title of “Developing Transparent Credit Risk Scorecards More Effectively: An Explainable Artificial Intelligence Approach”.

In this paper, the main focus is outcome (e.g., classification result) explanations of machine learning models for a specific instance and the explanation methods, by using and experimental A.I. framework that is straightforwardly composed by some well-known tools for ML-based A.I. explainability. This category of methods include rule-based methods (explain instances with simple logic rules) and attribution methods (which give an importance score for each input feature of the complex machine learning model). Rule-based outcome explanation methods, [ 16 ] are the first to introduce precision and generality as a requirement. i.e., Precision enforces that, if a rule explains an instance with a specific classification outcome (e.g., class 1), it should never explain other instances with a different classification outcome (e.g., class 0). And generality suggesting that, if a rule explains an instance with a particular classification outcome (e.g., class 1), it should also likely explain other instances having the same classification outcome. This makes precision and generality two important requirements that raise human trust in ML models explanations. However, these requirements are not tested or even implied in attribution methods, but they are defined and measured only on rules.

Machine Learning models are like black boxes that can only classify instances, where it is unknown how the classification procedure is performed. Hence, this paper provides an overview of model agnostic attribution methods along with a methodology on how to evaluate these method based on the precision and the generality of the attribution, and how to measure consistency between different generic attribution methods.

2. Model Agnostic Explanation Methods: An Introduction

Model agnostic methods separate the explanation from the ML model, which gives flexibility in using any interpretable ML method regardless of how the ML model is defined i.e., a model agnostic method uses the ML model as an oracle model. This category covers some basic approaches such as Dependency Plot (PDP) [ 17 ], Individual Conditional Expectation (ICE) [ 18 ], feature interaction based on H-statistic [ 19 ], and local surrogate models. Differently from other models, local surrogate ones focus on explaining a specific outcome of a single instance. Several related works in the field of machine learning are reported in [ 20 ]-[ 34 ].

We report in the following two relevant local surrogate models that are also attribution methods, i.e. LIME and SHAP, which provide for each feature of the classification model inputs an importance score. 2.1.

The First Explainability Tool: LIME

In order to explain an outcome of a model, LIME learns an interpretable model locally around the instance and modifies the data sample of a single instance by tweaking its feature values and observing how the changes affect the resulting output.

The main idea behind LIME is that: in order to understand the prediction sensitivity w.r.t. each feature of a particular instance, a “local sensitivity analysis” is performed on every outcome made by each individual instance that is passed on to the model. Figure 1 shows how LIME works theoretically.

The blue/orange background represents the original decision function i.e. clear to see that it is not linear, and the instance to explain is the largest red X mark . LIME simply generates new instances in the neighborhood of (i.e. perturbations) and assigns them weights based on their proximity to . The weights are represented in Figure 1 by the sizes of the symbols i.e. blue circles and red X marks. Based on the model’s outcome confidence on these perturbations, LIME approximates the complex model well by learning a linear model i.e. presented with a red line in Figure 1 locally around . It should be noted that, in this case, the explanation that LIME produces at a local point p is true only locally around the instance and not globally. The generic formula that returns this explanation is the following: ( ) = ∈ ( , , ) + ε( ) (1) where is the real function (known as the black box model i.e. the complex machine learning model to explain), is a surrogate model i.e. the simple model used to approximate locally around where defines this locality. This formulation can be applied with different surrogate explanation families , fidelity functions , and complexity measures . LIME assumes that complexity is opposed to explainability as usually belongs to the family of linear functions i.e. low in complexity. The loss function (i.e. fidelity function) minimizes the local mismatch between the complex machine learning model and the approximating function (i.e. the simple model), which is the well-known root mean square error loss function RMSE. Where, typically, is a linear combination of the input features of the predictive model.

LIME is considered as an attribution method by making use of a linear model, where the coefficients of this linear model are determining the importance scores for each feature. 2.2.

The Second Explainability Tool: SHAP

SHAP (SHaply Additive exPlanations) [ 36 ] is a unified approach introduced for interpreting model prediction from different interpretable techniques i.e. LIME [ 35 ], Shapley Sampling Values [ 37 ], DeepLIFT [ 38 ], QII [ 39 ], Layer-wise Relevance Propagation [ 40 ], Shapley Regression Values [ 41 ] by defining the class of additive feature attribution methods. SHAP assigns an importance value for each input feature by employing game theory in order to compute the attribution, particularly, by using the Shapley values. Which indicate the reward received by each player in a cooperative game for his participation in the coalition. Let be the set of all the input features of the ML model, given an instance and a complex ML model and by adopting Shapely values we obtain for each feature ∈ an attribution score ( ) as follows: ( , ) = ∑ | |! (| | − | | − 1)! ! [ ( ∪{ }) − ( )] (2) ⊆ ∖{ } where represents the confidence value of the complex ML model for a particular outcome (e.g., a specific class) and is the instance having each value [ ] of the feature ∈ \ substituted with the mean value of all values had among all the possible instances. This score indicates the relevance Models ( ) = 0 + ∑

∈ ∑ ( )( ( ) − ( ))2 ⊆ where ( ) is the kernel, and it is defined as ( ) = (| |)| |(| |−| |). | | | |−1 only a random sub-samples

⊂ { | ⊆ }.

All which allows this kernel to align SHAP with LIME. based machine learning models, e.g., Random Forest.

The speed up is obtained by optimizing the loss function ∑ ∈ ( )( ( ) − ( ))2 considering [ 42 ] provides a fast algorithm computation for SHAP in the context of explaining decision treeof the particular value assigned to each feature for the classification compared to the mean value of the feature in the instance .

Clearly, we see that the complexity of computing the feature score is exponential in the number of features. Therefore, approximations are provided in order to overcome such complexity.

Kernel SHAP [ 36 ], being one of these approximations, founds on fitting a linear model i.e. defined as follows:

This fitting procedure aims to minimize the loss function i.e. defined as follows: 3. How

To

Measure Precision, Generality, and Consistency of Attribution

In this Section, we describe how Precision, Generality, and Consistency are measured in attribution models using our methodology. In [ 16 ], precision and generality measurement methods for rules are already defined, but still not for attributions. In this Section, additionally, we propose a method for consistency measurement between two generic attribution techniques. 3.1.

Measuring Precision

It is enforced by Precision that, if a rule explains an instance with a specific classification outcome (e.g., class 1), it should never explain other instances with a different classification outcome (e.g., class 0). Thus, it is intuitive that, it is inconsistent and not trustable by a human to provide a rule that explains two different outcomes of a machine learning model. [ 16 ], measures inversely the precision of a rule that explains an outcome by the percentage of instances that obtain from the machine learning model a different outcome from and applies to those instances. In order to define precision to the attribution results, we introduce first two functions. ( ) of the values of the feature in . Given = 1, … , ( , ) which returns in ℝ| | a vector i.e. the selection the subset of features for each ∈ {1, … , }, attribution vector ( , )[ ] = [ ]. ( )

: ℝ → 2| | which returns the top-k feature according to . Let be the set of instances receiving the outcome and ¬ be the set of instances not receiving it, given an instance ∈ and its attribution the attribution precision using the Reverse Precision (RP) as follows: , we can inversely measure where = ( ( , ) = |{ ̂| ̂∈ ¬ , ( , ) = (

, ̂)}| | ¬ | ). It is intuitive that, using the reverse precision, we measure the percentage of instances that receive the outcome and have the same values of top-k features as the specifically explained instance. Given a particular outcome we can compute the average of the reverse precision scores at for each instance in as follows: ( ) = Σ ∈

( , | | ) (3) (4) (5) (6)

Measuring Generality

It is suggested by Generality that, if a rule explains an instance with a particular classification outcome (e.g., class 1), it should also likely explain other instances having the same classification outcome. Given two instances 1 and 2 along with their attribution vectors the function that measures how many top-k features does 1 and

2, we define have in common as follows: is already defined in the precision Section. Given an instance ∈ the

in the context of the top ℎ neighbour instances in of is measured , ({ , ( , , ℎ, ℎ( , ) return the top ℎ neighbour instances in where the function generality of its attribution using the function where

∈ { 3.3.

Measuring Consistency of . These different aggregation functions can provide us with more information about the commonalities of the attributions and their distribution among the top ℎ neighbor instances. It should be noted that the function does not consider the values of the features from the attributions, i.e., justified by the fact that, in the function, we use the only among the nearest neighbors, then we assume the similarity requirement of the values of these instances. Given a particular outcome the average of the generality scores at for the top-ℎ neighbour function instances for each instance in is computed as follows: 4.1.

The Datasets

The datasets used in the two attack detection contexts are described as follows. UNSW-NB 15: Network Traffic: Represents a comprehensive network-based dataset [ 43 ] that can reflect the network traffic’s modern scenarios, numerous types of low footprint intrusions, and depth structured information about this traffic. The IXIA PerfectStorm tool in the Cyber Range Lab of the Australian Centre for Cyber Security (ACCS) has created this raw network packets of this dataset that contains real normal behavior and synthesized attack activities of network traffic on Jan 22, 2015, and 15 hours on Feb 17,

As the attribution method SHAP unifies a number of other attribution methods, one of them is LIME, we propose a simple technique to compare the attribution between two different attribution methods. Given an instance and an attribution method , we denote the attribution scores for the instance provided by the attribution method

by Given the set of instances receiving an outcome and the two attribution methods 1 and 2 we define the consistency score for the top-k features between 1 and 2 as follows: ( , 1, 2) = Σ ∈

4. Experimental Evaluation and Analysis

In this Section, in order to evaluate attribution methods in two attack detection contexts, i.e., network traffic and power system. We apply our methodology focusing on the explanation (i.e. the attribution) of attack instances particularly. We start by describing the two datasets. Then, we display the classification results of different classification models in detecting such attacks. Finally, and after selecting the best classification model, and using our methodology, we evaluate LIME and SHAP attribution approaches in correctly interpreting attack instances that have been classified by this model. 2015 with a simulation period of 16 hours. This dataset consists of 2, 540, 044 records and contains 49 distinct features. ICS: Power System: captures different scenario of power system disturbance. This dataset [44] is a derivation from an original dataset containing 15 sets of 37 power system event scenario for each set (28 attack events and 9 normal events). It consists of a total of 128 features and 78, 377 records. (c) (d) Figure 2: “UNSW-NB 15” experimental patterns of: Linear Regression (a), Random Forest (b), KNN (c), and SVC (d) algorithms (c) (d) Figure 3: “ICS: Power System” experimental patterns of: Linear Regression (a), Random Forest (b), KNN (c), and SVC (d) algorithms 4.2.

Experimental Results

Before the start of the classification, we perform a one-hot encoding transformation on all the nonnumeric features. First, we split the dataset into a 70% training set and a 30% test set. The split was initially provided for “UNSW-NB 15” but with the same percentages. Then, we train and test the: Logistic Regression, Random Forest, KNN, Support Vector Classification (with RBF kernel) classification models. Figure 2 displays the classification results (Precision, Recall, F1-score and Accuracy) of all the classification models for “UNSW-NB 15”, and Figure 3 for “ICS: Power System”, respectively. We state that KNN and Random Forest provide the best and most comparable results. Finally, while applying our methodology in order to evaluate the attribution methods, we only concentrated on the Random Forest classifier as SHAP offers a more efficient computation.

Analysis of Attribution Precision

In Table 1 and Table 2 we show

( ) for LIME and SHAP when varying the number in “UNSW-NB 15” and “ICS: Power System”, respectively. We can see that, even for = 6, the values of the top-6 features, according to the attributions of the attack instances for both the methods (LIME and SHAP), are the same for the normal behavior in both the datasets. In fact, highlights the fact that as the explanation provided by LIME and SHAP for the attack instances also apply to normal behavior instances, then both LIME and SHAP are not really precise. Additionally, no attribution technique is better than the other. It is also interesting to see that according to the specific attribution procedure, the value of the top-1 most important feature is the same in numerous normal behavior instances, i.e. more than 70% in “UNSW-NB 15” and 50% in “ICS: Power System”. Intuitively, this shows how precision still remains an open problem for attribution methods. 6( ) > 0. Which 7 19 0 7 1 0 Figure 4:

(c) ( , , ℎ, Power System” (b), SHAP in “ICS: Power System” (c) and in “ICS: Power System” (d) ) by varying and ℎ for: LIME in “ICS: Power System” (a) and in “ICS: 4.4.

Analysis of Attribution Generality

Figure 4 (a) shows the values of ) by varying the number of top features and the number of close neighbors ℎ for LIME and Figure 4 (c) for SHAP in “UNSW-NB 15”, and Figure 4 (b) shows the average generality values for LIME, and Figure 4 (d) for SHAP in “ICS: Power System”, respectively. Based on the results, even the closest instances produce attributions that are drastically different. Therefore, the attributions of both methods is not so general and attribution seems unique for the specific instance rather than being generic. 4.5.

Analysis of Attribution Consistency

In this experiment, we show how LIME and SHAP are consistent, especially when considering SHAP as a method that unifies a number of other attribution methods including LIME. Figure 5 (a) shows ( , , ) when varying the number in “UNSW-NB 15” and Figure 5 (b) in “ICS: Power System” respectively. We can see that LIME and SHAP agree over less than third of the top-k features for both the datasets. Particularly, in terms of top-1, top-2, and top-3 features, where the methods have a strong disagreement.

This evaluation highlights the fact that the attributions provided by the two methods are different, and it is difficult to determine which attribution method is the best, as they have low performances in terms of precision and generality.

(b) ) by varying in: “UNSW-NB 15” (a), and “ICS: Power System” (b)

5. Conclusions and Future Work

Attribution methods are crucial for machine learning models interpretability evaluation. In this paper, we provided a new methodology to evaluate the precision, generality, and consistency of attribution methods. And, we applied it in order to evaluate the two common model agnostic attribution models, LIME and SHAP, on two attack classification tasks related to network traffic and power systems in the industrial control system field. Our methodology highlighted the lack of precision and generality in these two methods and the fact that no method is really better than the other. Regardless of SHAP being proposed as the unification model and that it should generalize LIME, we inspected the attribution results of the two attribution methods in numerous cases, and they were very different. Based on this evaluation, we came with a conclusion that there is no best model for attribution and that still more research is needed to overcome the limitations of precision and generality in this topic.

Future work has many aspects. One concerns with integrating the methodologies with emerging big data analytics tools, in different settings (e.g., [45-48]).

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