A Taxonomy of Explainable Bayesian Networks
DDerks I.P., de Waal A. (2020) A Taxonomy of Explainable Bayesian Networks. In: Gerber A. (eds)Artificial Intelligence Research. SACAIR 2021. Communications in Computer and Information Science,vol 1342. Springer, Cham. https://doi.org/10.1007/978-3-030-66151-9 14
A Taxonomy of Explainable Bayesian Networks
Iena Petronella Derks − − − and Alta deWaal , − − − Department of Statistics, University of Pretoria Center for Artificial Intelligence Research (CAIR)
Abstract
Artificial Intelligence (AI), and in particular, the explainabilitythereof, has gained phenomenal attention over the last few years. Whilstwe usually do not question the decision-making process of these systems insituations where only the outcome is of interest, we do however pay closeattention when these systems are applied in areas where the decisionsdirectly influence the lives of humans. It is especially noisy and uncertainobservations close to the decision boundary which results in predictionswhich cannot necessarily be explained that may foster mistrust amongend-users. This drew attention to AI methods for which the outcomes canbe explained. Bayesian networks are probabilistic graphical models thatcan be used as a tool to manage uncertainty. The probabilistic frameworkof a Bayesian network allows for explainability in the model, reasoningand evidence. The use of these methods is mostly ad hoc and not as wellorganised as explainability methods in the wider AI research field. Assuch, we introduce a taxonomy of explainability in Bayesian networks. Weextend the existing categorisation of explainability in the model, reasoningor evidence to include explanation of decisions. The explanations obtainedfrom the explainability methods are illustrated by means of a simplemedical diagnostic scenario. The taxonomy introduced in this paper hasthe potential not only to encourage end-users to efficiently communicateoutcomes obtained, but also support their understanding of how and,more importantly, why certain predictions were made.
Keywords:
Bayesian network · Reasoning · Explainability.
Advances in technology have contributed to the generation of big data in nearlyall fields of science, giving rise to new challenges with respect to explainability ofmodels and techniques used to analyse such data. These models and techniquesare often too complex; concealing the knowledge within the machine, hencedecreasing the extent of interpretability of results. Subsequently, the lack ofexplainable models and techniques contribute to mistrust among users in fieldsof science where interpretability and explainability are indispensable.To elucidate the need for explainable models, consider the following threescenarios. Firstly, suppose a medical diagnosis system is used to determinewhether a tumour sample is malignant or benign. Here, the medical practitioner a r X i v : . [ c s . A I] J a n IP Derks, A de Waal must be able to understand how and why the system reached the decision, and,if necessary, inspect whether the decision is supported by medical knowledge [2].Next, consider self-driving cars. In this context, the self-driving car must be ableto process information faster than a human, such that accidents and fatalitiescan be avoided [21]. Suppose a self-driving car is involved in an accident, thenthe system must be able to explain that in order to avoid hitting a pedestrian,the only option was to swerve out of the way and, by coincidence, into anothervehicle. Lastly, consider an online restaurant review system, where reviews areclassified as positive or negative based on the words contained in the review. Here,the classifier simply returns whether a review is positive or negative, withoutexplaining which words contributed to the classification. As such, negative reviewsthat are expressed in, for example, a sarcastic manner, might be classified aspositive, resulting in a restaurant receiving a higher rating and more diners – whomight experience bad service (or even food poisoning) as a result of mislabelledreviews.Given its relevance in many application areas, the explainability problemhas attracted a great deal of attention in recent years, and as such, is an openresearch area [24]. The manifestation of explainable systems in high-risk areashas influenced the development of explainable artificial intelligence (XAI) inthe sense of prescriptions or taxonomies of explanation. These include fairness,accountability, transparency and ethicality [3, 11, 23]. The foundation of such asystem should include these prescriptions such that a level of usable intelligenceis reached to not only understand model behaviour [1] but also understand thecontext of an application task [14]. Bayesian networks (BNs) – which lie at theintersection of AI, machine learning, and statistics – are probabilistic graphicalmodels that can be used as a tool to manage uncertainty. These graphicalmodels allow the user to reason about uncertainty in the problem domain byupdating ones beliefs, whether this reasoning occurs from cause to effect, orfrom effect to cause. Reasoning in Bayesian networks is often referred to aswhat-if questions. The flexibility of a Bayesian network allows for these questionsto be predictive, diagnostic and inter-causal. Some what-if questions might beintuitive to formulate, but this is not always the case especially on a diagnosticand inter-causal level. This might result in sub-optimal use of explainability inBNs - especially on an end-user level. Apart from well-established reasoningmethods, the probabilistic framework of a Bayesian network also allows forexplainability in evidence. These include most probable explanation and mostrelevant explanation. To extend on the existing explainability methods, wepropose an additional approach which considers explanations concerned with thedecision-base.In this paper, we research the current state of explainable models in AI andmachine learning tasks, where the domain of interest is BNs. In the currentresearch, explanation is often done by principled approaches to finding explana-tions for models, reasoning, and evidence. Using this, we are able to formulatea taxonomy of explainable BNs. We extend this taxonomy to include explana-tion of decisions. This taxonomy will provide end-users with a set of tools to
Taxonomy of Explainable Bayesian Networks 3 better understand predictions made by BNs and will therefore encourage efficientcommunication between end-users. The paper is structured as follows. We firstinvestigate the community and scope of explainability methods in Section 2.Thereafter, we introduce explanation in BNs, which includes the formulationof principled approaches, the theoretical properties associated therewith and ahands-on medical diagnosis example. Section 4 presents our newly formulatedtaxonomy of explainable BNs. The final section concludes the paper and includesa short discussion of future work.
In application areas where erroneous decisions have a direct impact on livelihood,relying on systems where the predictions cannot be explained may not be anoption. Explainability in such systems aids in establishing trust in not onlycircumstances where the system is used as a primary decision tool, but also caseswhere the system takes on a supportive role [28].Over the past few years, explainability in AI systems has gained immenseattention from the research community. This is reflected in the launch of variousevents and organisations. The Defense Advanced Research Projects Agency(DARPA) launched the Explainable Artificial Intelligence (XAI) initiative in2016. The XAI programs intention is to encourage the production of AI techniqueswhere emphasis is placed on developing more accurate and precise models, whilestill maintaining a high level of explainability. Ultimately, XAI systems mustbe able to explain their rationale and enable understanding [12]. Conferences,such as the International Joint Conferences on Artificial Intelligence (IJCAI)conducts workshops specifically focusing on XAI [26]. This topic has also made anoticeable appearance at the Neural Information Processing Systems (NeurIPS)conference, with panel discussions solely concentrating on XAI.The scope of explainability is inherently linked to the complexity of themodel, as well as the goal thereof. Usually, but not necessarily, there is a trade-offbetween model accuracy and explainability – the higher the accuracy, the lowerthe explainability [31]. For example, decision trees provide a clear explanationbut are often less accurate than deep learning models, which are less transparent.It should be mentioned that this trade-off is also connected to the quality ofdata. AI and machine learning models that are transparent by design, such aslinear regression, decision trees and k-nearest neighbours, convey a degree ofexplainability [1]. However, when AI and machine learning models do not provideclear explanations, separate explainability methods are applied to the modelto gain meaningful explanations. Methods of explainability are not limited tothe behaviour of the model or decision-making process as a whole, and may beapplied to single instances, predictions or decisions [6]. These explanations canbe in the form of visualisations or natural language [10]. Some of the existingexplainability methods are layer-wise relevance propagation (LRP), which areoften used in deep neural networks where the prediction made by the networkis propagated back into the neural network using a set of predefined rules [27].
IP Derks, A de Waal
Another explainability method is local interpretable model-agnostic explanations(LIME). LIME methods can be used to explain prediction instances by attemptingto understand the behaviour of the prediction function in the context of theprediction. Here, the user is able to obtain a local explanation for that particularinstance. LIME can also be used to obtain explanations for the entire model bygenerating multiple instances [17]. Methods of explainability are also extended todocument classifiers, where documents are classified based on predicted likelihood.Here, explanations can be produced based on a search through the text-spaceof possible word combinations – starting with a single word and expanding thenumber of words until an explanation is found [25].Uncertainty is present in the majority of AI fields, such as knowledge repres-entation, learning and reasoning [22]. Real-world data often contain noisy anduncertain observations close to the decision boundary, which may result in pre-dictions that cannot be explained [7]. Probabilistic graphical models can be seenas uncertainty management tools as they are able to represent and reason withuncertainty. These probabilistic models are often employed to support decisionmaking in various application fields, including legal and medical applications [29].One such probabilistic model is BNs, which is capable of combining expert know-ledge and statistical data, therefore allowing for complex scenarios to be modelled.However, not only are the inner workings of Bayesian networks complicated tomost end-users [15], the explanation of probabilistic reasoning is challenging andas such results appear to be counter-intuitive or wrong [16]. Therefore, thereexists a demand for explanation in Bayesian networks.Explanation methods for Bayesian networks can be divided into three broadapproaches. The first approach consists of presenting information contained inthe knowledge base and is known as explanation of the model . There are twoobjectives associated with this type of explanation. Firstly, explanation of themodel is used to assist application experts in the model-construction phase.Secondly, it is used for instructional purposes to offer knowledge about thedomain [19]. The objective of the second approach is to justify the conclusion andhow it was obtained. This approach is referred to as explanation of reasoning [9].The final approach, explanation of evidence , is concerned with the treatmentof the variables in the Bayesian network [13]. In explanation of evidence, alsoreferred to as abduction , an explanation is seen as the configuration of a portionof the variables present in the Bayesian network, given evidence. Not included inthe aforementioned explanation methods are techniques that describe whetherthe end-user is ready to make a decision, and if not, what additional informationis required to better prepare for decision making. Techniques such as sensitivityanalysis [4] and same-decision probability [5] provide the end-user with insighton decisions. We group these methods into a fourth approach, explanation ofdecisions . For the purpose of this paper, and accordingly, the formulation of theexplainable taxonomy, we only consider explanation of reasoning, evidence, anddecisions. Explanation of the model is excluded from this taxonomy – at the timebeing – as the intent of the taxonomy is to support understanding of how andwhy predictions were made and not on the model-construction itself.
Taxonomy of Explainable Bayesian Networks 5
We adapt the XAI terminology to the scope of BNs by defining the term XBN andthereby referring to explainable BNs. To illustrate XBN in Bayesian networks,consider the Asia network from Lauritzen and Spiegelhalter (1988) [20] as anexample.
Example statement:
Suppose a patient visits a doctor, complaining aboutshortness of breath (dyspnoea) ( D ). The patient is worried he might have lungcancer. The doctor knows that lung cancer is only one of the possible causesfor dyspnoea, and other causes include bronchitis ( B ) and tuberculosis ( T ).From her training, the doctor knows that smoking increases the probability oflung cancer ( C ) and bronchitis. Both tuberculosis and lung cancer would resultin an abnormal X-ray ( X ) result. Lastly, a recent visit to Asia might increasethe probability of tuberculosis, as the disease is more prevalent there than thepatient’s country of origin.From this example statement, the nodes and values are defined and then thegraphical structure of the BN is constructed. This is followed by the quantificationof the conditional probability tables (CPTs) for each node [18] . The final BN isillustrated in Figure 1. Now that the domain and uncertainty are representedin the BN, we will look into how to use the BN. Reasoning in BNs takes placeonce we observe the value of one or more variables and we want to condition onthis new information [18]. It is important to note that this information need notnecessarily flow in the direction of the arcs, and therefore, reasoning can occur inthe opposite direction of the arcs.Figure 1: Asia Bayesian network Suppose during the doctor’s appointment, the patient tells the doctor he is asmoker before any symptoms are assessed. As mentioned earlier, the doctor knowssmoking increases the probability of the patient having lung cancer and bronchitis.This will, in turn, also influence the expectation of other symptoms, such as theresult of the chest X-Ray and shortness of breath. Here, our reasoning is performedfrom new information about the causes to new beliefs of the effects. This type ofreasoning is referred to as predictive reasoning and follows the direction of thearcs in the network. Through predictive reasoning, we are interested in questionsconcerning what will happen . In some cases, predictive reasoning is not of greatinsight and it is often required to reason from symptoms (effect) to cause, whichentails information flow in the opposite direction to the network arcs. For example,bronchitis can be seen as an effect of smoking. Accordingly, we are interested incomputing P ( S | B ). This is referred to as diagnostic reasoning and is typicallyused in situations where we want to determine what went wrong . The final typeof probabilistic reasoning in BNs is inter-causal reasoning , which relates tomutual causes of a common effect – typically indicated by a v-structure in thenetwork. In other words, inference is performed on the parent nodes of a sharedchild node. Note that the parent nodes are independent of one another unlessthe shared child node is observed, a concept known as d-separation . From theAsia network, we observe a v-structure between Tuberculosis, Lung Cancer andTuberculosis or Cancer (see Figure 2a). Here, Tuberculosis is independent fromLung cancer. Suppose we observe the patient has either Tuberculosis or Cancer –indicated by the green (or light grey if viewed in grey-scale) bar in Figure 2b –then this observation increases the probabilities of the parent nodes, Tuberculosisand Lung Cancer. However, if it is then revealed that the patient does, in fact,have Tuberculosis it, in turn, lowers the probability of a patient having LungCancer (see Figure 2c). We can then say Lung Cancer has been explained away .It should be noted that the probabilistic reasoning methods discussed above canbe used as is, or can be combined to accommodate the problem at hand. Sometimes, users of the system find the results of reasoning unclear or questionable.One way to address this is to provide scenarios for which the reasoning outcomesare upheld. A fully specified scenario is easier to understand than a set ofreasoning outcomes. Explanation of evidence methods are useful in specifyingthese scenarios. They are based on the posterior probability and the generalisedBayes factor. Firstly, we focus on methods that aim to find a configuration ofvariables such that the posterior probability is maximised given the evidence.Here, we consider the Most Probable Explanation (MPE), which is a specialcase of the Maximum A Posteriori (MAP). The MAP in a BN is a variableconfiguration which includes a subset of unobserved variables in the explanationset such that the posterior probability – given evidence – is maximised. Similarly,if the variable configuration consists of all variables present in the explanation
Taxonomy of Explainable Bayesian Networks 7(a) Joint Probability Tables for T, C and P (b) Adding evidence to P(c) Adding evidence to T
Figure 2: Belief Updating for T, C and Pset, we have an MPE solution [13]. However, in some real-world applications,the variable set often consists of a large number of variables, which may resultin over-specified or under-specified explanations obtained from the MPE. Infact, only a few variables may be relevant in explaining the evidence. The nextapproach finds a single instantiation that maximises the generalised Bayes factorin a trans-dimensional space containing all possible partial instantiations. Inother words, this approach aims to obtain an explanation only consisting of themost relevant variables in the BN, given the evidence. This approach is knownas the Most Relevant Explanation (MRE) [32–34].
Most Probable Explanation
Let’s first consider the MPE method. Recallthat the MPE finds the complete instantiation of the target variables – which aredefined to be unobserved – such that the joint posterior probability is maximisedgiven evidence. Figure 3 shows the scenario (or case) that has the highest jointprobability in the Asia network. Note here the probabilities are replaced bythe likelihood of the variable state belonging to the most probable scenario, forexample, if we look at the two possible states for Bronchitis, we see that ‘False’,i.e., the patient does not have bronchitis, is more probable. Suppose we discoverthe patient suffers from shortness of breath, we can then set the evidence forDyspnoea as ‘True’ (illustrated in Figure 4). By introducing this new evidence,we now observe a slightly different scenario, where it is more probable for thepatient to be a smoker and have bronchitis. Notice here that variables thatseem irrelevant to the evidence explanation, such as Visit to Asia and XRay,are included in the explanation. This could lead to overspecified hypotheses,especially in larger networks.
IP Derks, A de Waal
Figure 3: Initial MPE for Asia Bayesian networkFigure 4: Updated MPE for Asia Bayesian network
Taxonomy of Explainable Bayesian Networks 9
Most Relevant Explanation
To avoid an overspecified hypotheses, one ap-proach is to trim or prune less relevant variables from the explanation. That is,instead of finding the complete instantiation of the target variables, a partialinstantiation of the target variables is found such that the generalised Bayesfactor is maximised. Let’s first consider the explanations obtained from thegeneralised Bayes factor. Again, suppose the patient suffers from shortness ofbreath (evidence). We are then interested in finding only those variables that arerelevant in explaining why the patient has shortness of breath. Table 1 containsthe set of explanations obtained from the generalised Bayes factor. For example,the last entry shows that a possible explanation for shortness of breath is a trip toAsia and an abnormal X-ray. Thus including only 2 variables from the remaining7 variables (excluding Dyspnoea). As mentioned, the MRE is the explanationthat maximises the generalised Bayes factor. From Table 1 we see that havingBronchitis best explains the shortness of breath. Notice that this explanationdoes not include Smoking, as opposed to the MPE which included Smoking.Thus, although smoking is a probable cause for shortness of breath, it is not themost relevant cause. An interesting characteristic of the MRE is its ability tocapture the explaining away phenomenon [33].Table 1: Explanations of GBF scores for Asia network
Explanation Generalised Bayes Factor (Bronchitis) 6.1391 (Smoker, Tuberculosis or Cancer) 1.9818(Tuberculosis or Cancer) 1.9771(Lung Cancer, Smoker) 1.9723(Lung Cancer) 1.9678(Smoker, Tuberculosis) 1.8896(Tuberculosis) 1.8276(Smoker, XRay) 1.7779(Smoker) 1.7322(Visit to Asia, XRay) 1.5635
Hidden or unobserved variables appear in most application fields, especiallyin areas where decisions made by the end-user directly influence human lives.For example, when first examining a patient, the health-state of the patient isunknown. In these situations, one would typically ask two questions. The firstbeing given the available information, are we ready to make a decision? andsecondly, if we are not yet ready to make a decision, what additional informationdo we require to make an informed decision? . To answer these questions, theauthors of [5] propose a threshold-based notion, named same-decision probability ,which provides the user with a confidence measure that represents the probability that a certain decision will be made, had information pertaining unknown vari-ables been made available. Another possible threshold-based solution to this issensitivity analysis [30]. In sensitivity analysis, the assessments for the conditionalprobabilities in the BN are systematically changed to study the effect on theoutput produced by the network. The idea is that some conditional probabilitieswill hardly influence the decisions, while others will have significant impact.
Same-decision Probability
Suppose we are interested in making a decisionon whether the patient is a smoker (Smoking), which is conditioned on evidenceTuberculosis or Cancer. We can then use the BN such that our decision pertainingto the hypothesis is supported on the basis that the belief in the hypothesis givensome evidence exceeds a given threshold. Now, the patient may have access toinformation that is unknown to us, for example, the patient recently visited Asiaand chose not to disclose this information. Therefore, we do not have access to thetrue state of this variable. The true state knowledge may confirm or contradictour decision based on the probability of smoking given some evidence and thepatient visiting Asia. If we now compare this probability with some threshold,we have a degree of confidence in our original decision regarding smoking andthe available evidence. Had the patient disclosed his trip to Asia, it is thenunlikely that we would have made a different decision. Hence, we can make useof the same-decision probability (SDP). Consider now the BN given in Figure 5.Notice here the addition of three nodes,
P(Smoker=True) , Decision Threshold and
Decision . Where
P(Smoker=True ) represents the hypothesis probability andthe decision threshold is set to 55%. Suppose now we update our network suchthat Tuberculosis or Cancer (P) is True – to reflect the scenario discussed above.The hypothesis probability then increases from 50.00% to 84.35% (see Figure 6).Our decision is confirmed given the threshold since the hypothesis probabilitynow exceeds the given threshold value. From Table 2, the SDP before addingevidence for the ‘True’ state is 0.00%. After adding evidence, the SDP for ourdecision is 83.88%, indicating that our decision confidence is 83.88% .Table 2: Decision Confidence for Asia network States Minimum Maximum Mean Standard DeviationNo evidence False 100.00% 100.00% 100.00% 0.00%True 0.00% 0.00% 0.00% 0.00%Evidence False 0.00% 100.00% 16.12% 36.77%True 0.00% 100.00% 83.88% 36.77% The SDP scenario was constructed using the decision node functionality in Bayesialab.The decision nodes are indicated as green (or dark grey if viewed in grey-scale). Taxonomy of Explainable Bayesian Networks 11
Figure 5: Addition of decision node in Asia networkFigure 6: Updated decision for Asia network
The point of XBN is to explain the AI task at hand. In other words, the questionthe decision-maker seeks to answer, and not the technique in principle. Therefore,we need to be able to freely ask ‘why’ or ‘what’ and from this select a methodthat would best address the AI task. In Figure 7 we present a taxonomy of XBN.The purpose of this taxonomy is to categorise XBN methods into four phases ofBNs: The first phase involves the construction of the BN model. Explanationin the ‘model’ phase is critical when the model is based on expert knowledge.The second phase is reasoning, the third phase evidence, and the fourth decision.Explanation of the model and sensitivity analysis are illustrated in grey as it isout of scope for this paper. Although we define the taxonomy along these phases,we do acknowledge that not all phases are necessarily utilised by the decision-maker. For example, when using BNs to facilitate participatory modelling [8],the main emphasis is on explaining the model. Or, when using BNs as a classifier,the emphasis is on explaining the decisions. In this section, we present typicalquestions of interest to the decision-maker in each category of the XBN taxonomy.Figure 7: A schematic view of XBN
Reasoning in the XBN taxonomy is concerned with the justification of a conclusion.Returning to our Asia example, the end-user might ask the following question,“
Given the patient recently visited Asia, how likely is an abnormal chestX-Ray? ” Taxonomy of Explainable Bayesian Networks 13
Here, we are concerned with a single outcome: the X-Ray result. On the otherhand, the doctor may have knowledge about symptoms presented by the patientand ask,“
What is the probability of a patient being a smoker, given that he presentedshortness of breath? ”We can extend this to a forensic context. Suppose a crime scene is investigatedwhere a severely burned body is found. The forensic analyst can then ask,“
The burn victim is found with a protruded tongue, was the victim exposedto fire before death or after? ”Consider now a financial service context where a young prospective home owneris declined a loan. The service provider can then ask,“
Did the prospective owner not qualify for the home loan because of his age? ”From these examples, we see that explanation of reasoning is used where questionsare asked in the context of single variable outcomes for diagnosis.
When we are interested in the subset of variables that describes specific scenarios,we use explanation of evidence methods. For example, in our Asia example thedoctor may ask,“
Which diseases are most probable to the symptoms presented by the patient? ”or “
Which diseases are most relevant to the symptoms presented by the patient? ”In a forensic context, the forensic analyst investigating a crime scene may askthe following question,“
What are the most relevant causes of death, given the victim is found with aseverely burned body and protruded tongue? ”Similarly this can be applied to fraud detection. Suppose the analyst investigatesthe credit card transactions of a consumer. The analyst can then ask,“
What are the most probable transaction features that contributed to theflagging of this consumer? ”Explanation of evidence can also be used to provide explanations for financialservice circumstances. For example, if a prospective home owner is turned downfor a loan, he may ask the service provider which features in his risk profile aremore relevant (contributed most) to being turned down.
Explanation of decisions typically asks the following questions “Do we haveenough evidence to make a decision?” , and if not, “what additional evidence isrequired to make a decision?” . For example, in our Asia example we can ask,“
Do we have enough evidence on the symptoms presented to make a decisionon the disease? ”or “
Since we are not yet able to determine the disease, what additional inform-ation – test, underlying symptoms, comorbidities – is required to make adecision? ”Applied to forensic investigations, this can be used to answer questions relatingto crime scene investigations. The analyst may ask questions regarding the actualevidence collected from the crime scene, i.e., if enough evidence is collected torule a crime as a homicide or what additional evidence is required to rule thecrime as a homicide. Should they investigate further or is the evidence that isalready collected enough to make an informed decision?
The development of AI systems has faced incredible advances in recent years. Weare now exposed to these systems on a daily basis, such as product recommend-ation systems used by online retailers. However, these systems are also beingimplemented by medical practitioners, forensic analysts and financial services– application areas where decisions directly influence the lives of humans. It isbecause of these high-risk application areas that progressively more interest isgiven to the explainability of these systems.This paper addresses the problem of explainability in BNs. We first exploredthe state of explainable AI and in particular BNs, which serves as a foundation forour XBN framework. We then presented a taxonomy to categorise XBN methodsin order to emphasise the benefits of each method given a specific usage of the BNmodel. This XBN taxonomy will serve as a guideline, which will enable end-usersto understand how and why predictions were made and will, therefore, be ableto better communicate how outcomes were obtained based on these predictions.The XBN taxonomy consists of explanation of reasoning, evidence and de-cisions. Explanation of the model is reserved for future work, since the taxonomydescribed in this paper is focused on how and why predictions were made and noton the model-construction phase. Other future research endeavours include theaddition of more dimensions and methods to the XBN taxonomy – this involvesmore statistical-based methods and the incorporation of causability (which alsoaddresses the quality of explanations) – as well as applying this taxonomy toreal-world applications.
Taxonomy of Explainable Bayesian Networks 15
References
1. Barredo Arrieta, A., D´ıaz-Rodr´ıguez, N., Del Ser, J., Bennetot, A., Tabik, S.,Barbado, A., Garcia, S., Gil-Lopez, S., Molina, D., Benjamins, R., Chatila, R.,Herrera, F.: Explainable Artificial Intelligence (XAI): Concepts, taxonomies, op-portunities and challenges toward responsible AI. Information Fusion , 82–115(2020). https://doi.org/10.1016/j.inffus.2019.12.0122. Brito-Sarracino, T., dos Santos, M.R., Antunes, E.F., de Andrade Santos, I.B.,Kasmanas, J.C., de Leon Ferreira, A.C.P., et al.: Explainable Machine Learning forBreast Cancer Diagnosis. In: 2019 8th Brazilian Conference on Intelligent Systems(BRACIS). pp. 681–686. IEEE (2019)3. Cath, C.: Governing artificial intelligence: Ethical, legal and technical op-portunities and challenges. Philosophical Transactions of the Royal SocietyA: Mathematical, Physical and Engineering Sciences (2133) (2018). ht-tps://doi.org/10.1098/rsta.2018.00804. Chan, H., Darwiche, A.: On the Robustness of Most Probable Explanations. Pro-ceedings of the 22nd Conference on Uncertainty in Artificial Intelligence, UAI 2006(06 2012)5. Choi, A., Xue, Y., Darwiche, A.: Same-decision probability: A confidence measurefor threshold-based decisions. International Journal of Approximate Reasoning (9), 1415–1428 (2012)6. Das, A., Rad, P.: Opportunities and Challenges in Explainable Artificial Intelligence(XAI): A Survey. arXiv preprint arXiv:2006.11371 (2020)7. De Waal, A., Steyn, C.: Uncertainty measurements in neural network predictionsfor classification tasks. In: 2020 IEEE 23rd International Conference on InformationFusion (FUSION). pp. 1–7. IEEE (2020)8. D¨uspohl, M., Frank, S., D¨oll, P.: A review of Bayesian networks as a participatorymodeling approach in support of sustainable environmental management. Journalof Sustainable Development (12) (2012). https://doi.org/10.5539/jsd.v5n12p19. Gallego, M.J.F.: Bayesian networks inference: Advanced algorithms for triangulationand partial abduction (2005)10. Goebel, R., Chander, A., Holzinger, K., Lecue, F., Akata, Z., Stumpf, S., Kieseberg,P., Holzinger, A.: Explainable AI: the new 42? In: International cross-domainconference for machine learning and knowledge extraction. pp. 295–303. Springer(2018)11. Greene, D., Hoffmann, A.L., Stark, L.: Better, Nicer, Clearer, Fairer: A CriticalAssessment of the Movement for Ethical Artificial Intelligence and Machine Learning.Proceedings of the 52nd Hawaii International Conference on System Sciences pp.2122–2131 (2019). https://doi.org/10.24251/hicss.2019.25812. Gunning, D., Aha, D.W.: DARPA’s explainable artificial intelligence program. AIMagazine (2), 44–58 (2019)13. Helldin, T., Riveiro, M.: Explanation Methods for Bayesian Networks: review andapplication to a maritime scenario. In: Proc. of The 3rd Annual Sk¨ovde Workshopon Information Fusion Topics, SWIFT. pp. 11–16 (2009)14. Holzinger, A., Malle, B., Kieseberg, P., Roth, P.M., M¨uller, H., Reihs, R., Zatloukal,K.: Towards the Augmented Pathologist: Challenges of Explainable-AI in DigitalPathology. arXiv preprint arXiv:1712.06657 pp. 1–34 (2017), http://arxiv.org/abs/1712.0665715. Keppens, J.: Explaining Bayesian Belief Revision for Legal Applications. In: JURIX.pp. 63–72 (2016)6 IP Derks, A de Waal16. Keppens, J.: Explainable Bayesian network query results via natural languagegeneration systems. In: Proceedings of the Seventeenth International Conferenceon Artificial Intelligence and Law. pp. 42–51 (2019)17. Khedkar, S., Subramanian, V., Shinde, G., Gandhi, P.: Explainable AI in Healthcare.In: Healthcare (April 8, 2019). 2nd International Conference on Advances in Science& Technology (ICAST) (2019)18. Korb, K.B., Nicholson, A.E.: Bayesian Artificial Intelligence. CRC press (2010)19. Lacave, C., D´ıez, F.J.: A review of explanation methods for Bayesiannetworks. Knowledge Engineering Review (2), 107–127 (2002). ht-tps://doi.org/10.1017/S026988890200019X20. Lauritzen, S.L., Spiegelhalter, D.J.: Local computations with probabilities ongraphical structures and their application to expert systems. Journal of the RoyalStatistical Society: Series B (Methodological) (2), 157–194 (1988)21. Lawless, W.F., Mittu, R., Sofge, D., Hiatt, L.: Artificial Intelligence, Autonomy,and Human-Machine Teams: Interdependence, Context, and Explainable AI. AIMagazine (3), 5–13 (2019)22. Lecue, F.: On the role of knowledge graphs in explainable AI. Semantic Web (1),41–51 (2020)23. Leslie, D.: Understanding artificial intelligence ethics and safety: A guide for theresponsible design and implementation of AI systems in the public sector (Jun2019). https://doi.org/10.5281/zenodo.324052924. Lipton, Z.C.: The mythos of model interpretability. Queue (3), 31–57 (2018)25. Martens, D., Provost, F.: Explaining data-driven document classifications. MISQuarterly (1), 73–100 (2014)26. Miller, T., Weber, R., Magazzeni, D.: Proceedings of the IJCAI 2019 Workshop onExplainable AI (2019)27. Montavon, G., Binder, A., Lapuschkin, S., Samek, W., M¨uller, K.R.: Layer-wiserelevance propagation: an overview. In: Explainable AI: interpreting, explainingand visualizing deep learning, pp. 193–209. Springer (2019)28. Samek, W., M¨uller, K.R.: Towards explainable artificial intelligence. In: ExplainableAI: interpreting, explaining and visualizing deep learning, pp. 5–22. Springer (2019)29. Timmer, S.T., Meyer, J.J.C., Prakken, H., Renooij, S., Verheij, B.: A two-phasemethod for extracting explanatory arguments from Bayesian networks. InternationalJournal of Approximate Reasoning , 475–494 (2017)30. Van Der Gaag, L.C., Coup´e, V.M.: Sensitivity analysis for threshold decision makingwith bayesian belief networks. In: Congress of the Italian Association for ArtificialIntelligence. pp. 37–48. Springer (1999)31. Xu, F., Uszkoreit, H., Du, Y., Fan, W., Zhao, D., Zhu, J.: Explainable AI: ABrief Survey on History, Research Areas, Approaches and Challenges. LectureNotes in Computer Science (including subseries Lecture Notes in Artificial In-telligence and Lecture Notes in Bioinformatics) , 563–574 (2019).https://doi.org/10.1007/978-3-030-32236-6 5132. Yuan, C.: Some properties of most relevant explanation. In: ExaCt. pp. 118–126(2009)33. Yuan, C., Lim, H., Lu, T.C.: Most relevant explanation in bayesian net-works. Journal of Artificial Intelligence Research42