After clinical decision support systems are validated and deployed, one is often reluctant to update the model with new insights or data, especially if this means that re-certification is required. In this paper we address this issue in updating Bayesian networks with new domain knowledge. More specifically, we introduce and study the concept of safe inverse marginalisation, an operation that allows for adding new variables to a network without affecting the distribution over the original variables. As such, the additional efforts required for validation and certification can be limited, re-using as much as possible the analyses and documentation from the original model. To support the process of safely extending a Bayesian network, we present an algorithm that flags potentially unsafe updates.
In multi-label classification (MLC), each instance can be assigned to none, one or multiple labels from a predefined label set, and the task is to predict the relevant subset of labels for each new instance. A common challenge in MLC is class imbalance, which often leads to biased classifiers that underestimate rare labels. In this paper, we propose a framework that combines probabilistic classifier chains (PCC) with a minimax learning strategy based on the Discrete minimax classifier. PCC allows us to model label dependencies and optimize various loss functions, including the subset 0/1 loss, Hamming loss, and F1-measure, while the minimax learning strategy mitigates the class imbalance problem by minimizing and balancing the class conditional risks. We conduct experiments on ten benchmark datasets using multiple models of different learning strategies. Our analysis focuses on the ability of models to optimize a loss function while also reducing the false positive and false negative rates. To this end, we use two complementary metrics designed to measure imbalance in class-conditional accuracies.
Quantum logic (QL) has been developed using various methods. Among them, orthomodular lattices and binary relational models have been discussed as models that concisely express the logic of quantum mechanics. Although these models are compatible with mathematical logic, some elements are still missing. In this study, a new binary relational model that introduces the concept of inner product in a Hilbert space is proposed. We also propose dynamic extended quantum logic (DEQL), which is the logic based on the new model, and prove some of the usefulness of the model and logic.
This paper studies the use of distortions as a tool for addressing conflicts between a finite number of uncertainty models, in the general case where these initial models may not be precise, in particular a lower probability. We propose to distort the associated credal sets until the global conflict is removed, and to use the conjunction aggregation rule in that moment. We investigate this procedure in the case where the distortion is made using the total variation distance, and compare its properties with other aggregation rules from the literature. In addition, we also explore an alternative where the distortion is tweaked so as to enlarge the credal sets only in the directions where conflict is present.
This paper investigates updating methods for possibility measures and their logical representation through conditional operators. We introduce a general possible worlds semantics equipped with selection functions (or equivalently, Boolean algebras with binary conditional operators). This provides a unified framework for various conditionals, including those studied by Stalnaker and Lewis. Building on our recent triviality result-which shows standard conditionalization for possibility measures cannot be represented as the possibility of a given conditional-we explore how alternative updating methods for possibility measures can be represented as the possibility of conditionals within our framework. Specifically, we define novel updating methods for possibility measures based on these selection functions. These methods, unlike standard conditionalization, exhibit a direct correspondence with the possibility of conditionals. In particular, we prove the possibility of selection function-based conditionals directly aligns with updated qualitative capacities, as defined by Dubois et al. Furthermore, we delineate the specific conditions under which the possibility of such conditionals precisely coincides with a general update of the original possibility measure.
Forgetting is a method used in several formalisms of knowledge representation and reasoning, which removes some elements from a framework while preserving the rest of the framework as much as possible. This paper investigates the process of forgetting in ASPIC(+), a structured argumentation framework. We explore possible effects of forgetting operators on several levels, namely: effects on (1) the underlying language, (2) arguments and their conclusions, and (3) the justification statuses of arguments' conclusions. We define the desired behaviour for forgetting formulas in a variant of ASPIC(+), drawing from both practical considerations and existing research on forgetting in other frameworks. Furthermore, for a specific modification of the standard ASPIC(+) framework, we managed to define two concrete forgetting operators, and evaluate them against the set of desiderata.
Probabilistic opinion pooling aims to aggregate the probabilistic beliefs of multiple agents to reach a consensus. When dealing with high uncertainty contexts, agents' beliefs are often represented by imprecise probabilities, i.e. intervals of probability values. The most commonly used aggregation method for imprecise opinion pooling is linear pooling, which takes a weighted average of the input opinions. However, determining an optimal weight distribution for pooling is a complex challenge. In this work, we propose a novel elicitation method inspired by epistemic voting that provides probabilistic guarantees for agents to hold a correct belief. Furthermore, we show how to derive well-performing pooling weights from the elicited beliefs using existing results for the voting rule on which our elicitation method is based. Finally, we carry out parametric simulations that illustrate the whole process of elicitation and weighting and that show an increase in the quality of the aggregated opinions.
This paper studies the problem of quantifying the robustness level of explanations. In particular, we propose to quantify the robustness level of each given explanation as the maximum level of perturbation on the parameters of a classifier below which an explanation remains valid. We derive theoretical results on the computational complexity of determining the robustness level in the case of linear models, which underpin the design of a log-linear time algorithm. We then apply the proposed notion of robustness level to analyze the robustness of commonly used specific types of prime implicants, including the shortest and the most robust ones. The insights are then leveraged to construct guidelines on scenarios where each type of explanations may be more beneficial.
In this work, we propose using possibility theory to represent a belief base and to reason over it, particularly in the presence of inconsistencies. We revisit semantics from the existing literature and introduce two additional properties that help to clarify how these semantics are interconnected. The framework is then restricted to hypotheses expressed as linear numerical inequalities, in order to benefit from the polynomial-time complexity of Linear Programming while maintaining possibilistic reasoning. Finally, we define certified inference syntaxes based on Farkas' Lemma, allowing a certificate to be provided for each inference.
This paper proposes a quantification method to support the elicitation process for Bayesian network construction. The method aims at reducing the number of subjective modelling choices that need to be made to arrive at an initial quantification of a Bayesian network. Our method allows domain experts to express their knowledge in the form of probability constraints. Then, exploiting recent insights concerning the computation of entropy in Bayesian networks, it uses the Maximum Entropy principle to determine a single quantification that makes no assumptions beyond the information provided by the domain experts. The quantification can be used in an iterative probability elicitation process. We provide an overview of our maximum entropy-based quantification method, detail how to express experts' constraints for this technique for entropy maximisation and illustrate the method using an example.
A general extended disjunctive logic program (GEDP) with negation as failure in the head may have non-minimal answer sets, while answer sets of an extended disjunctive logic program (EDLP) are minimal. So far, no work has been done to relate general extended disjunctive logic programming and assumption-based argumentation (ABA). In this paper, first, we propose a novel polynomial-time translation from a GEDP to an EDLP, with which there is a one-to-one correspondence between the consistent answer sets of the original GEDP and those of the translated EDLP. Second, based on the proposed translation as well as the work to relate EDLPs and ABA frameworks (ABFs), we show a one-to-one correspondence between the consistent answer sets of a consistent propositional GEDP and the consistent stable extensions of its associated ABF.
Strongly admissible labelings and min-max numberings offer well-founded explanations in formal argumentation. We establish a precise correspondence between min-max numberings and remoteness functions from combinatorial game theory, showing that min-max numbers characterize optimal play length, i.e., where players seek the fastest win or longest delay of loss. Our game–argumentation duality strengthens the theoretical and computational foundations for cross-fertilization between argumentation and game theory: game-theoretic provenance explanations apply to argumentation frameworks; pure strategy-based provenance aligns with strongly admissible labelings; and a linear-time algorithm for computing remoteness is sufficient to compute grounded labelings and min-max numbers.
We provide a generalisation of Kripke semantics for Monadic first-order Basic Logic of Chains ( MBLC ) of Petr Hájek and prove its soundness and completeness with respect to our semantics. This paper extends the insights of [10] from BL to the case of MBLC .
Restricted Boltzmann Machines (RBMs) are bipartite graphical models with binary latent and observed variables that have shown promise for representation learning. However, their lack of interpretable parameters limits their utility in domains requiring explainability, like educational assessment. Despite extensive RBM research, nonnegativity constraints on weights-essential for monotonicity in educational contexts-remain largely unexplored. To address this, we propose a method to translate RBMs into a specialized class of bipartite Bayesian networks, which we term BN2A networks, characterized by strict 2-layer separation (hidden and observed variables), Noisy-AND conditional probability tables, and directly interpretable parameters for educational models. Our work establishes a mathematical transformation from RBM weights to BN2A's interpretable parameters (leak and penalty probabilities), theoretical analysis showing BN2A's constrained connectivity is a subset of RBM architectures, and empirical evidence that the transformation preserves model fidelity under realistic conditions. By bridging these paradigms, our method leverages RBM's representational power while achieving BN2A's interpretability, opening new possibilities for adaptive learning systems and diagnostic tools.
Power grids depend on precise power measurements for various operational, economic, and security decisions. Wrong measurement data can lead to wrong or delayed decisions, ultimately wasting resources. This paper examines the detection of wrong data in active power measurements for distribution grids using Bayesian networks. Both supervised and unsupervised approaches are explored, where the supervised approach learns a Naive Bayes-type classifier from labeled active power measurements data, while the unsupervised method utilizes unlabeled data in conjunction with a surprise index (data conflict measure) to identify unusual data. An experimental analysis is conducted using a real-world dataset from a medium-voltage grid, where multiple types of anomalies are injected into the time series of active power data. The supervised model demonstrates high detection rates and short delays, while the performance of the unsupervised approach is promising.
Analogical proportions are relations that link 4 items a, b, c and d and that are expressed as "a is to b as c is to d". These 4 items are often described by vectors of Boolean, nominal, or numerical values. Analogical proportions can however relate logical formulas. The article proposes a first study of analogical proportions between probabilities, whether they are simply between values, or between distributions (which requires the preservation of their normalization). The properties of definitions based on arithmetic proportion, or combining the latter with geometric proportion are studied, and potential uses are described. An appendix proposes a proof of the Pythagorean theorem in terms of geometric proportions.
We propose a novel approach to understanding conditional statements, viewing them as change descriptors within a standard nondeterministic framework. Our logical systems operate on a tree ordering, where the past is linear but the future is inherently uncertain and branching. We provide an axiomatization and demonstrate completeness for systems incorporating both a solely forward-looking conditional operator and a combination of backward and forward-looking operators. Additionally, we introduce and prove analogous results for the duals of these conditional operators, which naturally represent update operators by detailing the transformations leading to the current state.
Logistic regression (LR) is one of the most commonly used classification models in Machine Learning. Even though LR was shown to be asymptotically the best linear classifier, it can typically be at the cost of high variance when the sample size is small compared to the number of predictive variables. Moreover, LR models are extremely sensitive to outliers. The influence of outliers has traditionally been handled by using weighted LR so that data points considered not to be outliers have a weight equal to 1, whilst those considered outliers are assigned a lower weight, which is typically computed from some distance measure over the training data. In this paper, we propose a novel iterative procedure for estimating the parameters of an LR model that automatically accounts for the presence of outliers by following an expectation maximization (EM) approach. During the expectation step, each training data point is weighted according to its probability of being an outlier; in the maximization step, the parameters of the LR model and the outlier probabilities are updated. We have experimentally validated our proposal using a set of well-established benchmark datasets for classification. The results of the experiments show that, in addition to being computationally tractable, our new method outperforms both plain LR and several outliers detection methods, in terms of accuracy and logarithmic loss.
We propose compiling Bayesian networks (BNs) into arithmetic circuits (ACs) using symbolic probabilistic inference (SPI). Traditionally, ACs have been compiled from BNs using variable elimination (VE). A key advantage of SPI is its ability to combine product terms that VE would not. When the BN exhibits specific topological structures, SPI produces significantly smaller ACs than VE, addressing the core concern of circuit size in knowledge compilation. We also introduce the notion of indicator-determined buckets (IDBs) in ACs. These are sets of AC nodes that take on two exclusive values: zero or a fixed probability value. We present a method for identifying and leveraging them to construct more compact circuits. Experimental results on benchmark BNs demonstrate that combining SPI with IDB optimization yields a noticeable reduction in circuit size and in the time required for exact inference compared to inference using an AC compiled with VE.
Multi-agent decision-making under uncertainty can be modelled using partially observable stochastic games (POSGs), with numerous agents, partial observability, stochastic dynamics, and individual goals. However, POSGs are notoriously difficult to solve due to their exponential dependence on the number of agents. In this work, we present counting POSGs using the lifting technique of counting to compactly encode symmetries in a POSG, which enables using representative policies. We exploit the encoding for a counting version of the multi-agent dynamic programming operator to solve such a POSG. Doing so reduces the exponential dependence on the number of agents to a polynomial one, making the problem tractable with respect to agent numbers.
