the date of receipt and acceptance should be inserted later Abstract In a criminal trial, evidence is used to draw conclusions about what happened concerning a supposed crime. Traditionally, the three main approaches to modeling reasoning... more
the date of receipt and acceptance should be inserted later Abstract In a criminal trial, evidence is used to draw conclusions about what happened concerning a supposed crime. Traditionally, the three main approaches to modeling reasoning with evidence are argumentative, narra-tive and probabilistic approaches. Integrating these three approaches could arguably enhance the communication between an expert and a judge or jury. In previous work, techniques were proposed to represent narratives in a Bayesian network and to use narratives as a basis for systematizing the construction of a Bayesian network for a legal case. In this paper, these techniques are combined to form a design method for constructing a Bayesian network based on narratives. This design method is evaluated by means of an extensive case study concerning the notorious Dutch case of the Anjum murders.
This thesis presents a method to create an explanation for the reasoning of Bayesian networks in order to explain the most probable value for the node of interest. The first part identifies a set of intermediate nodes which are nodes that... more
This thesis presents a method to create an explanation for the reasoning of Bayesian networks in order to explain the most probable value for the node of interest. The first part identifies a set of intermediate nodes which are nodes that can explain the most probable value of the node of interest. These intermediate nodes act as a funnel for the node of interest and summarize the evidence nodes. This set of intermediate nodes is found by the Edmonds-Karp algorithm in combination with one of three weight-assignment functions. One of these functions is purely based on the structure of the graph of the Bayesian network and the other two different functions take the probability distributions of the Bayesian network into account as well. The second part gives arguments that explain the most probable values of the intermediate nodes by creating clusters, which are set of nodes that include at least one evidence node of the Bayesian network. The actual explanation takes the output of thes...
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This paper provides a formal description of two legal domains. In addition, we describe the generation of various artificial datasets from these domains and explain the use of these datasets in previous experiments aligning learning and... more
This paper provides a formal description of two legal domains. In addition, we describe the generation of various artificial datasets from these domains and explain the use of these datasets in previous experiments aligning learning and reasoning. These resources are made available for the further investigation of connections between arguments, cases and rules. The datasets are publicly available at https://github.com/CorSteging/LegalResources.
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Bayesian networks (BNs) are powerful tools that are increasingly being used by forensic and legal experts to reason about the uncertain conclusions that can be inferred from the evidence in a case. Although in BN construction it is good... more
Bayesian networks (BNs) are powerful tools that are increasingly being used by forensic and legal experts to reason about the uncertain conclusions that can be inferred from the evidence in a case. Although in BN construction it is good practice to document the model itself, the importance of documenting design decisions has received little attention. Such decisions, including the (possibly conflicting) reasons behind them, are important for legal experts to understand and accept probabilistic models of cases. Moreover, when disagreements arise between domain experts involved in the construction of BNs, there are no systematic means to resolve such disagreements. Therefore, we propose an approach that allows domain experts to explicitly express and capture their reasons pro and con modelling decisions using argumentation, and that resolves their disagreements as much as possible. Our approach is based on a case study, in which the argumentation structure of an actual disagreement between two forensic BN experts is analysed.
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The justification of an algorithm’s outcomes is important in many domains, and in particular in the law. However, previous research has shown that machine learning systems can make the right decisions for the wrong reasons: despite high... more
The justification of an algorithm’s outcomes is important in many domains, and in particular in the law. However, previous research has shown that machine learning systems can make the right decisions for the wrong reasons: despite high accuracies, not all of the conditions that define the domain of the training data are learned. In this study, we investigate what the system does learn, using state-of-the-art explainable AI techniques. With the use of SHAP and LIME, we are able to show which features impact the decision making process and how the impact changes with different distributions of the training data. However, our results also show that even high accuracy and good relevant feature detection are no guarantee for a sound rationale. Hence these state-of-the-art explainable AI techniques cannot be used to fully expose unsound rationales, further advocating the need for a separate method for rationale evaluation.
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In this paper, we propose the information graph (IG) formalism, which provides a precise account of the interplay between deductive and abductive inference and causal and evidential information. IGs formalise analyses performed by domain... more
In this paper, we propose the information graph (IG) formalism, which provides a precise account of the interplay between deductive and abductive inference and causal and evidential information. IGs formalise analyses performed by domain experts using the informal reasoning tools they are familiar with, such as mind maps used in crime analysis. Based on principles for reasoning with causal and evidential information given the evidence, we impose constraints on the inferences that may be performed with IGs. Moreover, we propose an argumentation formalism based on IGs that allows arguments to be formally evaluated.
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A Hidden Markov model (HMM) is a frequently applied statisti cal model for capturing processes that evolve over time. The parameters specified in a HMM are often inaccur ate, and sensitivity analyses can be employed to study the effects... more
A Hidden Markov model (HMM) is a frequently applied statisti cal model for capturing processes that evolve over time. The parameters specified in a HMM are often inaccur ate, and sensitivity analyses can be employed to study the effects of these inaccuracies on the outp ut of a model. In the context of HMMs, sensitivity analysis is usually performed by means of a perturbat ion analysis where a small change is applied to the parameters, upon which the output of interest is re-comp uted [2]. Recently, however, it was shown that a simple mathematical function describes the relation betw e n HMM parameters and an output probability of interest [1]. This result was established by representin g the HMM as a (Dynamic) Bayesian network; for determining the so-called sensitivity function, it was suggested to use existing algorithms for sensitivity analysis in Bayesian networks. The drawback of this approac h is that the repetitive character of the HMM, with the same parameters occurring for ...
In this paper, we propose a structured approach for transforming legal arguments to a Bayesian network (BN) graph. Our approach automatically constructs a fully specified BN graph by exploiting causality information present in legal... more
In this paper, we propose a structured approach for transforming legal arguments to a Bayesian network (BN) graph. Our approach automatically constructs a fully specified BN graph by exploiting causality information present in legal arguments. Moreover, we demonstrate that causality information in addition provides for constraining some of the probabilities involved. We show that for undercutting attacks it is necessary to distinguish between causal and evidential attacked inferences, which extends on a previously proposed solution to modelling undercutting attacks in BNs. We illustrate our approach by applying it to part of an actual legal case, namely the Sacco and Vanzetti legal case.
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In the context of evidence evaluation, where the probability of evidence given a certain hypothesis is considered, different pieces of evidence are often combined in a naive way by assuming conditional independence. In this paper we... more
In the context of evidence evaluation, where the probability of evidence given a certain hypothesis is considered, different pieces of evidence are often combined in a naive way by assuming conditional independence. In this paper we present a number of results that can be used to assess both the importance of a reliable likelihood-ratio estimate and the impact of neglecting dependencies among pieces of evidence for the purpose of evidence evaluation. We analytically study the effect of changes in dependencies between pieces of evidence on the likelihood ratio, and provide both theoretical and empirical bounds on the error in likelihood occasioned by assuming independences that do not hold in practice. In addition, a simple measure of influence strength between pieces of evidence is proposed.
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Probabilistic relational models (PRMs) extend Bayesian networks beyond propositional expressiveness by allowing the representation of multiple interacting classes. For a specific instance of sets of concrete objects per class, a ground... more
Probabilistic relational models (PRMs) extend Bayesian networks beyond propositional expressiveness by allowing the representation of multiple interacting classes. For a specific instance of sets of concrete objects per class, a ground Bayesian network is composed by replicating parts of the PRM. The interactions between the objects that are thereby induced, are not always obvious from the PRM. We demonstrate in this paper that the replicative structure of the ground network in fact constrains the space of possible probability distributions and thereby the possible patterns of intercausal interaction.
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In this paper, we propose an argumentation formalism that allows for both deductive and abductive argumentation, where ‘deduction’ is used as an umbrella term for both defeasible and strict ‘forward’ inference. Our formalism is based on... more
In this paper, we propose an argumentation formalism that allows for both deductive and abductive argumentation, where ‘deduction’ is used as an umbrella term for both defeasible and strict ‘forward’ inference. Our formalism is based on an extended version of our previously proposed information graph (IG) formalism, which provides a precise account of the interplay between deductive and abductive inference and causal and evidential information. In the current version, we consider additional types of information such as abstractions which allow domain experts to be more expressive in stating their knowledge, where we identify and impose constraints on the types of inferences that may be performed with the different types of information. A new notion of attack is defined that captures a crucial aspect of abductive reasoning, namely that of competition between abductively inferred alternative explanations. Our argumentation formalism generates an abstract argumentation framework and th...
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Bayesian networks have gained popularity as a probabilistic tool for reasoning with legal evidence. However, two common difficulties are (1) the construction and (2) the understanding of a network. In previous work, we proposed to use... more
Bayesian networks have gained popularity as a probabilistic tool for reasoning with legal evidence. However, two common difficulties are (1) the construction and (2) the understanding of a network. In previous work, we proposed to use narrative tools and in particular scenario schemes to assist the construction and the understanding of Bayesian networks for legal cases. We proposed a construction method and a reporting format for explaining or understanding the network. The quality of a scenario, which plays an important role in the narrative approach to evidential reasoning, was not yet included in this method. In this paper, we provide a discussion of what constitutes the quality of a scenario, in terms of the narrative concepts of completeness, consistency and plausibility. We propose a probabilistic interpretation of these concepts, and show how they can be incorporated in our previously proposed method. We also illustrate with an example how these concepts concerning scenario q...
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Causal interaction models, such as the well-known noisy-or and leaky noisy-or models, have become quite popular as a means to parameterize conditional probability tables for Bayesian networks. In this paper we focus on the engineering of... more
Causal interaction models, such as the well-known noisy-or and leaky noisy-or models, have become quite popular as a means to parameterize conditional probability tables for Bayesian networks. In this paper we focus on the engineering of subnetworks to represent such models and present a novel technique called recursive unfolding for this purpose. This technique allows inserting, removing and merging cause variables in an interaction model at will, without affecting the underlying represented information. We detail the technique, with the recursion invariants involved, and illustrate its practical use for Bayesian-network engineering by means of a small example.
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The same-decision probability (SDP) is a confidence measure for threshold-based decisions. In this paper we detail various properties of the SDP that allow for studying its robustness to changes in the threshold value upon which a... more
The same-decision probability (SDP) is a confidence measure for threshold-based decisions. In this paper we detail various properties of the SDP that allow for studying its robustness to changes in the threshold value upon which a decision is based. In addition to expressing confidence in a decision, the SDP has proven to be a useful tool in other contexts, such as that of information gathering. We demonstrate that the properties of the SDP as established in this paper allow for its application in the context of explaining Bayesian network classifiers as well.
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Bayesian networks typically require thousands of probability para-meters for their specification, many of which are bound to be inaccurate. Know-ledge of the direction of change in an output probability of a network occasioned by changes... more
Bayesian networks typically require thousands of probability para-meters for their specification, many of which are bound to be inaccurate. Know-ledge of the direction of change in an output probability of a network occasioned by changes in one or more of its parameters, i.e. the qualitative effect of parameter changes, has been shown to be useful both for parameter tuning and in pre-processing for inference in credal networks. In this paper we identify classes of parameter for which the qualitative effect on a given output of interest can be identified based upon graphical considerations.
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Legal reasoning with evidence can be a challenging task. We study the relation between two formal approaches that can aid the construction of legal proof: argumentation and Bayesian networks (BNs). Argument schemes are used to describe... more
Legal reasoning with evidence can be a challenging task. We study the relation between two formal approaches that can aid the construction of legal proof: argumentation and Bayesian networks (BNs). Argument schemes are used to describe recurring patterns in argumentation. Critical questions for many argument schemes have been identified. Due to the increased use of statistical forensic evidence in court it may be advantageous to consider probabilistic models of legal evidence. In this paper we show how argument schemes and critical questions can be modelled in the graphical structure of a Bayesian network. We propose a method that integrates advantages from other methods in the literature.
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Causal interaction models such as the noisy-or model, are used in Bayesian networks to simplify probability acquisition for variables with large numbers of modelled causes. These models essentially prescribe how to complete an... more
Causal interaction models such as the noisy-or model, are used in Bayesian networks to simplify probability acquisition for variables with large numbers of modelled causes. These models essentially prescribe how to complete an exponentially large probability table from a linear number of parameters. Yet, typically the full probability tables are required for inference with Bayesian networks in which such interaction models are used, although inference algorithms tailored to specific types of network exist that can directly exploit the decomposition properties of the interaction models. In this paper we revisit these decomposition properties in view of general inference algorithms and demonstrate that they allow an alternative representation of causal interaction models that is quite concise, even with large numbers of causes involved. In addition to forestalling the need of tailored algorithms, our alternative representation brings engineering benefits beyond those widely recognised.
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In this paper, we propose a way to derive constraints for a Bayesian Network from structured arguments. Argumentation and Bayesian networks can both be considered decision support techniques, but are typically used by experts with... more
In this paper, we propose a way to derive constraints for a Bayesian Network from structured arguments. Argumentation and Bayesian networks can both be considered decision support techniques, but are typically used by experts with different backgrounds. Bayesian network experts have the mathematical skills to understand and construct such networks, but lack expertise in the application domain; domain experts may feel more comfortable with argumentation approaches. Our proposed method allows us to check Bayesian networks given arguments constructed for the same problem, and also allows for transforming arguments into a Bayesian network structure, thereby facilitating Bayesian network construction.
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Upon varying parameters in a sensitivity analysis of a Bayesian network, the standard approach is to co-vary the parameters from the same conditional distribution such that their proportions remain the same. Alternative co-variation... more
Upon varying parameters in a sensitivity analysis of a Bayesian network, the standard approach is to co-vary the parameters from the same conditional distribution such that their proportions remain the same. Alternative co-variation schemes are, however, possible. We theoretically investigate the effects of using alternative co-variation schemes on th e so-called sensitivity function, and conclude that its general form remains the same under any linear co-variation scheme. In addition, we generalise the CD-distance for bounding global belief change, and prove a tight lower bound on this distance for parameter changes in single conditiona l probability tables.
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A Bayesian network is a concise representation of a joint probability distribution, which can be used to compute any probability of interest for the represented distribution. Credal networks were introduced to cope with the inevitable... more
A Bayesian network is a concise representation of a joint probability distribution, which can be used to compute any probability of interest for the represented distribution. Credal networks were introduced to cope with the inevitable inaccuracies in the parametrisation of such a network. Where a Bayesian network is parametrised by defining unique local distributions, in a credal network sets of local distributions are given. From a credal network, lower and upper probabilities can be inferred. Such inference, however, is often problematic since it may require a number of Bayesian network computations exponential in the number of credal sets. In this paper we propose a preprocessing step that is able to reduce this complexity. We use sensitivity functions to show that for some classes of parameter in Bayesian networks the qualitative effect of a parameter change on an outcome probability of interest is independent of the exact numerical specification. We then argue that credal sets ...
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Research Interests: Mathematics, Computer Science, Artificial Intelligence, Statistics, Argumentation, and 11 moreExplanation, Inference, Argumentation Theory, Bayesian Networks, Probabilistic Logic, Uncertainty, Probabilistic reasoning, Bayesian Network, Approximate Reasoning, Numerical Analysis and Computational Mathematics, and Bayesian Probability
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This special issue of the International Journal of Approximate Reasoning is devoted to a selection of papers presented at the Twelfth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU... more
This special issue of the International Journal of Approximate Reasoning is devoted to a selection of papers presented at the Twelfth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2013), which took place in Utrecht, The Netherlands, on July 7th to July 10th, 2013.1 In total, 89 manuscripts were submitted to the conference. After a rigorous review process, 44 of the 89 submissions were accepted for presentation at the conference. Eight papers were selected for plenary presentation to do justice to their high quality. All accepted papers were published in the Springer Lecture Notes in Computer Science[1]. Based upon the scientific quality and the potential for extension of their contribution, the authors of nine papers were invited to submit a revised version of their paper to this special issue. Seven submissions were received from these nine invitations and went through the full reviewing process following the IJAR standards. Finally, six papers were accepted for publication in this special issue. The diversity of these six papers reflects the wide scope of the different approaches to reasoning under uncertainty covered by the community of ECSQARU. Three papers concern different aspects of a probabilistic approach, whereas the other three papers deal with non-probabilistic approaches
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Research Interests: Mathematics, Computer Science, Artificial Intelligence, Modeling, Inference, and 15 moreAbstraction, Causality, Algorithm, Cognitive Map, Probabilistic Logic, Cognitive Mapping, Levels of Abstraction, Bayesian Network, Probabilistic Neural Network, Approximate Reasoning, Numerical Analysis and Computational Mathematics, Bayesian Belief Network, Elsevier, Adaptive Algorithm, and Polynomial Time
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Qualitative probabilistic networks have been designed for probabilistic reasoning in a qualitative way. As a consequence of their coarse level of representation detail, qualitative probabilistic networks do not provide for resolving... more
Qualitative probabilistic networks have been designed for probabilistic reasoning in a qualitative way. As a consequence of their coarse level of representation detail, qualitative probabilistic networks do not provide for resolving trade-offs and typically yield ambiguous results upon inference. We present an algorithm for computing more informative results for unresolved trade-offs. The algorithm builds upon the idea of zooming in on the truly ambiguous part of a qualitative probabilistic network and identifying the information that ...
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This demonstration shows how arguments, formalised in a well defined framework, can be automatically constructed from a given Bayesian network.