In this paper we study everyday explanations for classification tasks with formal argumentation. Everyday explanations describe how humans explain in day-to-day life, which is important when explaining decisions of AI systems to lay users. We introduce EVAX, a model-agnostic explanation method for classifiers with which contrastive, selected and social explanations can be generated. The resulting explanations can be adjusted in their size and retain high fidelity scores (an average of 0.95).
why rather than ?; selected, not all possible explanations are returned, but rather just one or two are selected based on a cognitive bias, such as abnormality or responsibility; and social, explanations (e.g., their size or content) are adjusted to the receiver. • faithfulness: when explaining the outcome of a black box, learning-based system, it should be faithful to the system and its mechanisms.
In order to model the above properties in an argumentative explanation method, we introduce EVAX, an argumentative explanation method for everyday explanations of decisions derived with a classifier. EVAX is a model-agnostic method, which only requires the input and output of a classifier and can then compute, faithfully, explanations which are contrastive, selected and social.
The paper is structured as follows. Section 2 contains the preliminaries after which EVAX is introduced (Section 3). We present a quantitative (Section 4) and qualitative (Section 5) evaluation. Related work is discussed in Section 6 and we conclude in Section 7.
In this section we recall the necessary preliminaries on formal argumentation and classification tasks and present our definition of arguments and defeats.
An abstract argumentation framework (AF) [
In abstract argumentation, arguments are abstract entities and the attack relation is
predetermined. In contrast, in structured argumentation [
Definition 2. An argument is a triple (, , ), where is the premise (e.g., a feature), denoted by prem() = , is the conclusion inferred from (e.g., a class), denoted by conc() = and is the strength value of the argument, denoted by str() = where 0 ≤ ≤ 1.
Based on the structure of the arguments, the defeat relation is determined: Definition 3. Let ℱ = ⟨Args, Def⟩ be an AF and , ∈ Args. Then (, ) ∈ Def if conc() ̸= conc() and str() ≥ str().
As mentioned in the introduction, in this paper we are interested in explaining the outcome of
a classification task with argumentation. Intuitively, classification is an inference task in which
it is checked whether an object (e.g., an image, sound or text file) belongs to a category [
Example 1. Let 1, . . . , 6 ∈ , where every ∈ is a student, and let = {0, 1}, where 1 represents a student being accepted to university, and 0 a rejection. The set of features consists of {, , } ∈ ℱ , where corresponds to the (rounded) average grade of the student, to whether or not the student passed the entry test and to whether or not they are motivated. Suppose that we are given the following input space: 1 2 3 4 5 6 A classification task is then to determine whether student 6 is accepted or not.
In this paper, we are interested in everyday explanations as described in [
Additionally, the explanations should remain faithful to the model (i.e., they explain the behavior of the model accurately).
Our method EVAX takes as input a trained black box model and constructs a global set of arguments: for each feature and each class it determines the probability that input containing will be assigned . For a specific input point, consisting of a set of features, a local argumentation framework is created (i.e., only containing the arguments corresponding to features from that input point and the defeats between them), from which the conclusion is predicted. This local argumentation framework can then be used to derive explanations, the size of which can be set by the user. We have implemented two ways to present explanations: based on abnormality and in a dialogue form.
We start by describing the method of EVAX (Section 3.1), we will illustrate it with a toy example in Section 3.2.
EVAX takes as input a labeled dataset, a trained black box model BB and a threshold value select that controls the size of the output. EVAX returns a set of predictions pred and a set of local explanations ℰ . The explanations ∈ ℰ answer the question: “Why did black box BB assign class to input instance ?” These explanations are deployments of an argumentation framework that represent the behavior of BB around a single datapoint in argumentative terms. This AF thus forms the basis for the explanations, and will, for every classified instance, be referred to as ℱ . The size of ℱ can be manually altered by select.
Algorithm 1 EVAX 1: procedure EVAX(BB, labeled_dataset, select = 20) 2: train, test, train, test ← split_dataset(labeled_dataset, test_size = 0.2) 3: global_arguments ← get_global_arguments(BB, train) 4: for in test do 5: ℱ ← create_local_AF(, global_arguments, select) 6: predict(ℱ ) 7: explain(ℱ ) 8: results() 9: get_results(BB, predictions, test) ◁ step 1 ◁ step 2 ◁ step 3 ◁ step 4
The procedure of EVAX is shown in Algorithm 1.1 First, EVAX divides the labeled dataset into a set of unlabeled datapoints (the input space) and a set of labels (the target space), which are then split up into a train set and a test set, respectively train, test and train, test. The default size of the test set is 0.2, and the default select value is 20. Afterward, the method can be divided into four main steps, which are described below. The first step handles all datapoints 1See https://github.com/jowanvanlente/EVAX for the implementation. and is executed just once, whereas the other three steps handle a single datapoint and may be repeated multiple times, up to a maximum of the size of the test set.
• Step 1: Extract a global list of arguments, to represent the global behavior of BB. • Step 2: Create a local AF, ℱ .
– EVAX first iterates over all features (, ) ∈ ℱ of all (unlabeled) datapoints ∈ train and all output classes ∈ , and computes for every feature-class pair a decision rule. These rules are accompanied by a precision score (,) that articulates the probability that BB will assign a datapoint with that particular feature to that particular class. It then saves all (,) scores in a triple ((, ), , (,)), which is added to a list of triples. – Arguments are constructed based on the list of triples. For every triple an argument is constructed in which the feature (, ) is the premise prem, the output-class is the conclusion conc and the precision score (,) is set as the argument strength str. Together these arguments form the global list of arguments. – EVAX creates a local AF: ℱ in every iteration of this step. This is an argumentation framework ℱ = ⟨Args, Def⟩ that represents the classifier’s behavior around one particular datapoint. Based on the values of that datapoint, it selects a set of relevant arguments (Args ⊆ Args) from the global list of arguments (Args) and determines the defeats (Def). – Argument selection is done by matching the features of the datapoint from test with the premises of the arguments: given a datapoint ∈ test and an argument ∈ Args, if prem() is one of the features in then is added to the local AF (meaning ∈ Args). As a result, all arguments with a premise corresponding to one of the features of the datapoint are selected. To gain computational eficiency and maintain selectedness, a threshold select can be defined, which ensures only the top select strongest arguments are included in the list.
– The defeats are determined as in Definition 3. • Step 3: Predict the output class based on ℱ .
– First, the grounded extension of the local AF (Grd(ℱ )) is computed, after which
the conclusion of the arguments in Grd(ℱ ) is picked as the prediction. Formally,
this means that prediction ∈ is equal to conc() such that ∈ Grd(ℱ ).
Since arguments in the grounded extension are non-conflicting, they always have
the same conclusion. Therefore it does not matter what argument in Grd(ℱ ) is
picked. When Grd(ℱ ) is empty, EVAX will predict the majority class.
• Step 4: Explain
– The current implementation allows for two variations: adding selectedness based
on abnormality and presenting the explanation in a conversational form.
– Abnormality is one of the methods humans use when selecting an explanation
and describes how people tend to choose a cause that is unusual [
‘1 is poisonous because of its unusual pungent odor’
– EVAX can also provide a dialectical representation of ℱ , similar to a dispute
tree [
O: a93: gill-color = 4 → 0 (0.84) P: a16: gill-size = 1 → 1 (0.91)
O: since gill color is black, it is likely 1 has class edible
P: since gill size is narrow, it is likely 1 has class poisonous O: a143: spore-print-color = 2 → 0 (0.87)
O: since spore print color is black, it is likely 1 has class edible P: a130: odor = 6 → 1 (1.0)
P: since odor is pungent, it is certain 1 has class poisonous 2The only requirement of the counterargument is a conflicting conclusion, and not necessarily a higher strength value, i.e., it does not have to defeat the argument. This is to ensure that counterarguments are included in this explanation form.
Recall the classification task described in Example 1, on students being accepted into university. In Figure 3 we present a similar case to illustrate EVAX. It represents one iteration of Steps 2, 3, and 4. It thus assumes that the global list of arguments has already been computed.
In this example, a black box predicts that an input instance ‘John’ will be accepted into university. The same input instance is used as input for EVAX. Based on that input, EVAX creates a local argumentation framework ℱ by selecting three relevant arguments, based on the three diferent features, and defines defeats over them. It then calculates the grounded extension and predicts that John will be accepted into university. In addition, it computes an AF-based explanation, which in this case is a dialectical representation of ℱ , as described in Step 4. The threshold explain has a value of 3. The arrows in the representation are the defeats. Note that the arrows between the diferent components of EVAX do not represent defeats, but indicate the information flow.
O: John is motivated, therefore he usually gets accepted
P: John has grade 6, therefore he usually gets declined
O: John passed the test, therefore it is certain he gets accepted
John
Grade: 6 Passed test: yes Motivated: yes black-box
EVAX
ℱ 1: (grade < 8) → declined (0.7) 2: (passed test = yes) → accepted (1.0) 3: (motivated = yes) → accepted (0.6)
Defeats: (1, 3), (2, 1)
P: 3 O: 1
P: 2 accepted accepted
fidelity calculator
We have tested EVAX on four datasets and used five quantitative metrics for the evaluation.
The (labeled) datasets are from the UCI Machine Learning Repository [
The discretization of continuous variables is necessary to constrain the number of arguments
that are added to the global list of arguments. We have used the method by pandas [
For each of these datasets we have chosen four diferent machine learning models with
diferent complexity to test the performance and range of EVAX : logistic regression, support
vector machines (SVM), random forest, and neural networks. All four models are initialized
from the scikit-learn library [
Finally, we applied the following five metrics for the evaluation: • Fidelity indicates how well the explanation approximates the prediction of the black box model. It represents the fraction of datapoints that are assigned to the same output class by EVAX and BB. • Accuracy ( BB) indicates how well our model performs on unseen data. It represents the fraction of correctly classified datapoints. The value between brackets () refers to the original accuracy of BB. • Size measures the average minimum amount of arguments necessary to retain the same prediction. In other words, it is the lowest possible select score without afecting the accuracy or fidelity. A consistent low size value indicates the method can guarantee to compute small explanations that are consistently faithful. • Empty Grd specifies the fraction of datapoints for which the grounded extension Grd(ℱ ) is an empty set. When Grd(ℱ ) is an empty set, EVAX relies on a default prediction. A higher ‘Empty Grd’ value thus means that accuracy and fidelity scores are increasingly determined by the default prediction, and therefore become less reliable. • Time indicates the number of seconds needed to run the program.
The results in Table 1 show high fidelity (an average of 0.95) for all four ML models, which indicates a suficient degree of faithfulness. Only the adult dataset and the neural network of the wine dataset have relatively low scores. This might be due to the relatively low accuracy of the BB in those cases. Since the argument with the highest argument strength is always in Grd(ℱ ), the minimum size is always equal to 1. This indicates that the model is capable of computing small explanations without losing faithfulness. Moreover, we see that the method never computes an empty grounded extension Grd(ℱ ), and hence requires no reliance on a Adult Mushroom Iris Wine
Logistic regression
SVM Random forest
Neural network Logistic regression
SVM Random forest Neural network Logistic regression
SVM Random forest Neural network Logistic regression
SVM Random forest Neural network default prediction. These results are obtained on a Windows 64-bit operating system with 16GB RAM and an Intel(R) Core(TM) i5-1145G7 @ 2.60GHz processor.
The purpose of EVAX is the modeling of explanations as described in [
Contrastive explanations explain the fact (e.g., ) by highlighting its diferences with the foil
(e.g., ), by answering the question why rather than ? [
While an event might have infinitely many causes, humans are able to select one or two as
the explanation. To this end a variety of cognitivie biases are employed [
Finally, explanations are social, since the explainer will adapt the explanation to the explainee, for example, by adjusting the size, the content or the form of the explanation. Explanations can be adjusted in two ways with EVAX. First, the number of arguments that are included in ℱ can be adjusted with select and the size of the explanation can be adjusted with explain. In that way, an inexperienced end-user who requires a single argument to explain the prediction can set select = explain = 1. A more experienced user who wants a completer set of arguments and counterarguments can set higher values. Second, because a computed explanation ∈ ℰ stems from an AF, the explanation can be presented in various ways. In the current paper we have illustrated one of these representations in Figure 2, in the form of a dialogue.
As the survey [
Closest related to our work is [22, 23]. There several agents engage in a dialogue, by putting forward arguments in the form of classification association rules. This dialogue results in a tree of arguments and counterarguments. The result is an overview of the agents’ point of view, with arguments that might contain several premises. Given the focus on the dialogue and the structure of arguments and counterarguments, [22, 23] provide social and contrastive explanations. Our approach also aims at minimal explanations: our arguments have only one premise, the size of the explanation can be adjusted and the selection of the arguments in the explanation can be based on argument strength or abnormality. The purpose of our work (i.e., providing small, everyday explanations) is therefore diferent.
Following our interpretation of the explanations in [
In contrast, EVAX provides a method which is contrastive (arguments and counterarguments
are part of the explanation), selected (the maximum size can be reduced to one argument
and the selection of this argument can be based on abnormality) and social (the size of the
explanation can be adjusted and the explanation can be represented as a dialogue). Since
the explanations provided by EVAX rely on an argumentation framework, in future work
we can look at representing them as dispute trees (as in [
We have introduced EVAX an argumentative explanation method for everyday explanations
for classifiers. It takes as input a trained classifier, calculates a local argumentation framework
ℱ and can present explanations in a variety of ways (recall Figure 3). In particular, we have
shown how explanations can be selected, based on abnormality and how explanations can
be represented as a dialogue between proponent and opponent. Although the method might
seem somewhat naive, our results show that it is a fast explanation method, which satisfies our
requirements. Based on the quantitative results (recall Table 1) we have shown that our method
is faithful. Moreover, in the qualitative evaluation (Section 5), we have discussed how EVAX
produces everyday explanations that satisfy the findings from [
The results in this paper show that EVAX is a promising explanation method, which can be explored further. First, the properties of everyday explanations can be further worked out by including counterfactual statements, incorporating more cognitive biases, and testing more explanation deployments. Second, experimental evaluations with human users would more closely assess the quality of argumentative explanations. Elsevier, 2019, pp. 271–280. [22] M. Wardeh, T. Bench-Capon, F. Coenen, PADUA: a protocol for argumentation dialogue using association rules, Artificial Intelligence and Law 17 (2009) 183–215. [23] M. Wardeh, F. Coenen, T. Bench-Capon, Pisa: A framework for multiagent classification using argumentation, Data & Knowledge Engineering 75 (2012) 34–57. [24] A. Borg, F. Bex, Necessary and suficient explanations for argumentation-based conclusions, in: J. Vejnarová, N. Wilson (Eds.), Proceedings of the 16th European Conference of Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU, 2021, volume 12897 of Lecture Notes in Computer Science, 2021, pp. 19–31.