Article
History & Philosophy Of Science
Nicholas J. J. Smith
Summary: This paper presents a model of degrees of belief based on Dempster-Shafer belief functions and argues for belief functions over imprecise probabilities as a model of evidence-respecting degrees of belief. The arguments cover three aspects: theoretical virtues, motivations, and problem cases.
Article
Computer Science, Artificial Intelligence
Serafin Moral-Garcia, Joaquin Abellan
Summary: Belief functions and reachable probability intervals are theories based on imprecise probabilities that have different characteristics and applications. By studying the conditions and properties related to their association, a better understanding of their applications in addressing uncertainty can be achieved.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2021)
Article
Engineering, Mechanical
Dimitrios G. Giovanis, Michael D. Shields
Summary: The objective of this study is to quantify the uncertainty in probability of failure estimates resulting from incomplete knowledge of the probability distributions for the input random variables. The study proposes a framework that combines Subset Simulation (SuS) with Bayesian/information theoretic multi-model inference, and through methods such as multi-model inference and importance sampling, empirical probability distributions of failure probabilities that provide direct estimates of the uncertainty in failure probability estimates are obtained.
PROBABILISTIC ENGINEERING MECHANICS
(2022)
Article
Engineering, Mechanical
Jiaxin Zhang, Stephanie TerMaath, Michael D. Shields
Summary: This paper proposes a new framework to quantify uncertainties in probability model-form and model parameters resulting from small datasets, and integrates these uncertainties into Sobol' index estimates. Imprecise Sobol' indices are calculated from candidate probability models using an importance sampling reweighting method, providing a measure of confidence in sensitivity estimates and guiding data collection efforts. The approach is demonstrated through examples involving Timoshenko beam parameters and E-glass fiber composite material properties.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Computer Science, Artificial Intelligence
Serafin Moral-Garcia, Joaquin Abellan, Tahani Coolen-Maturi, Frank P. A. Coolen
Summary: The study introduces a new cost-sensitive Decision Tree model for Imprecise Classification, which considers error costs by weighting instances. Unlike traditional models, this method utilizes the Nonparametric Predictive Inference Model to provide more informative predictions.
APPLIED SOFT COMPUTING
(2022)
Article
Multidisciplinary Sciences
Tuan D. Pham
Summary: Image analysis in histopathology is crucial for disease diagnosis, prognosis, and biomarker discovery, with precise classification being the ultimate goal. The TF-TS LSTM network is applied for classifying histopathological images, utilizing sequential time-frequency and time-space features for deep learning. Results show strong capability in accurate classification across various datasets, indicating the potential of this approach as an AI tool for robust classification of histopathological images.
SCIENTIFIC REPORTS
(2021)
Article
Automation & Control Systems
Javier G. Castellano, Serafin Moral-Garcia, Carlos J. Mantas, Maria D. Benitez, Joaquin Abellan
Summary: A Bayesian Network is a graphical structure with conditional probability tables that allows for calculating probabilities between different features, particularly useful in credit scoring and risk analysis.
INTERNATIONAL JOURNAL OF FUZZY SYSTEMS
(2021)
Article
Computer Science, Artificial Intelligence
Jaemin Yoo, Junghun Kim, Hoyoung Yoon, Geonsoo Kim, Changwon Jang, U. Kang
Summary: In this work, the authors propose a novel graph-based positive-unlabeled (PU) learning method called GRAB, which requires no class prior. They further generalize GRAB to multi-positive unlabeled (MPU) learning. Experimental results demonstrate that GRAB achieves state-of-the-art performance on several real-world datasets, even without the true prior information given to competitors.
KNOWLEDGE AND INFORMATION SYSTEMS
(2022)
Article
Engineering, Mechanical
Lechang Yang, Sifeng Bi, Matthias G. R. Faes, Matteo Broggi, Michael Beer
Summary: In this paper, a novel entropy-based metric utilizing Jensen-Shannon divergence is proposed to address inverse problems with mixed uncertainty, showing effectiveness and efficiency. By employing a discretized binning algorithm to reduce computation cost, the method demonstrates promising results in both static and dynamic systems.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Computer Science, Artificial Intelligence
Bernhard Schmelzer
Summary: This paper investigates the probabilistic information induced by two random sets and a copula, focusing on the joint distributions of random variables contained in the random sets with the same copula, as well as the distributions covered by a random set in product space constructed from the marginal random sets and the copula. The results show that for the special case when the marginal random sets are probability boxes, there exists a subset relationship between the credal sets, and the lower and upper probabilities coincide on cylindrical sets. The paper also presents new findings on random sets in the real line and random intervals and their joint distribution.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2023)
Article
Multidisciplinary Sciences
Antoine Baker, Indaco Biazzo, Alfredo Braunstein, Giovanni Catania, Luca Dall'Asta, Alessandro Ingrosso, Florent Krzakala, Fabio Mazza, Marc Mezard, Anna Paola Muntoni, Maria Refinetti, Stefano Sarao Mannelli, Lenka Zdeborova
Summary: Research suggests that probabilistic risk estimation can enhance the performance of digital contact tracing, aiding in mitigating the impact of epidemics.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2021)
Article
Automation & Control Systems
Jeremias Knoblauch, Jack Jewson, Theodoros Damoulas
Summary: The paper advocates for an optimization-centric view of Bayesian inference, introducing the Rule of Three (ROT) as a generalized method for Bayesian posteriors. It also explores the applications of Generalized Variational Inference (GVI) posteriors and their potential to improve robustness and posterior marginals in Bayesian Neural Networks and Deep Gaussian Processes.
JOURNAL OF MACHINE LEARNING RESEARCH
(2022)
Article
Engineering, Electrical & Electronic
Yuanchun Zhao, Wenli Zhu, Ming Yang, Mengxia Wang
Summary: This paper proposes an imprecise conditional probability estimation method based on the Bayesian network theory for predicting wind power ramp events. The method constructs a BN using MWST and GS, and estimates parameters using an extended IDM to quantify the probability of random ramp events. Experimental results demonstrate the effectiveness of the proposed method in reliably predicting ramp events even with limited samples.
JOURNAL OF MODERN POWER SYSTEMS AND CLEAN ENERGY
(2021)
Article
Mathematics
Jose Manuel Gutierrez
Summary: The conditional probability formula accurately updates probability assignments when new information is added. It is proven that this formula is the only transformed probability measure that satisfies the minimum requirement relational assumption, using a non-atomic probability measure. This result is applicable to the standard Bayesian parametric model.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2023)
Article
Computer Science, Artificial Intelligence
Martin Magris, Alexandros Iosifidis
Summary: The last decade has seen a growing interest in Bayesian learning, but its technicality and complexity in practical implementations have limited its widespread adoption. This survey introduces the principles and algorithms of Bayesian Learning for Neural Networks from a practical perspective, discussing standard and recent approaches for Bayesian inference. It also explores the use of manifold optimization as a state-of-the-art approach and provides pseudo-codes for implementation.
ARTIFICIAL INTELLIGENCE REVIEW
(2023)
Article
History & Philosophy Of Science
Marco Zaffalon, Enrique Miranda
Summary: Recent work has formally linked the axiomatisation of incomplete preferences with the theory of desirability in the context of imprecise probability, showing that they are essentially the same theory. The equivalence has been established under the constraint of a finite set of possible prizes. This paper relaxes this constraint, creating one of the most general theories of rationality and decision making, and discusses the role of conglomerability as a rationality requirement.
Article
Computer Science, Artificial Intelligence
Arianna Casanova, Enrique Miranda, Marco Zaffalon
Summary: This study develops joint foundations for social choice and opinion pooling using coherent sets of desirable gambles, and provides new perspectives on traditional social choice results. It argues that weak Pareto should be considered a rationality requirement, discusses the aggregation of experts' opinions based on probability and utility, and highlights the limitations of this framework with implications for statistics. The connection between the results of this study and earlier works in the literature is also explored.
ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
(2021)
Article
Physics, Multidisciplinary
Alessio Benavoli, Alessandro Facchini, Marco Zaffalon
Summary: The 'weirdness theorem' reveals that weirdness arises in the form of negative probabilities or non-classical evaluation functionals when logic has bounds due to the algorithmic nature of its tasks. This clash between unbounded and bounded views of computation in logic is not logical inconsistency, but an expression of the conflict.
FOUNDATIONS OF PHYSICS
(2021)
Article
Computer Science, Artificial Intelligence
Arianna Casanova, Juerg Kohlas, Marco Zaffalon
Summary: In this paper, we establish a connection between desirability and information algebras by showing how coherent sets of gambles and coherent lower previsions induce such structures. This approach allows us to treat imprecise-probability objects as algebraic and logical structures, and provides tools for manipulation.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2022)
Article
Computer Science, Artificial Intelligence
Arianna Casanova, Juerg Kohlas, Marco Zaffalon
Summary: This paper discusses the construction and generalization of information algebra, as well as its connection to set algebras and propositional logic. It also explores how propositional logic can naturally be embedded into the theory of imprecise probabilities.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2022)
Article
Computer Science, Artificial Intelligence
Alessio Benavoli, Alessandro Facchini, Marco Zaffalon
Summary: This study demonstrates that the symmetrisation postulate regarding identical particle systems corresponds to the assessment of exchangeability for observables in quantum experiments, and discusses the update of exchangeable observable sets after a measurement and the definition of entanglement for indistinguishable particle systems.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2022)
Article
Computer Science, Artificial Intelligence
Arianna Casanova, Alessio Benavoli, Marco Zaffalon
Summary: This paper presents the interpretation of standard desirability and other instances of nonlinear desirability as a classification problem. By analyzing different sets of rationality axioms, the paper shows the possibility of reformulating the problem as a binary classification problem and demonstrates the use of machine learning techniques to define a feature mapping and solve the problem in higher-dimensional spaces.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2023)
Article
Computer Science, Artificial Intelligence
Manuel Schuerch, Dario Azzimonti, Alessio Benavoli, Marco Zaffalon
Summary: Gaussian processes (GPs) are widely used in machine learning and statistics, but their computational complexity limits their applicability to datasets with only a few thousand data points. To overcome this limitation, we propose a new approach based on aggregating predictions from multiple local and correlated experts, which can provide consistent uncertainty estimates. Our method can handle various kernel functions and multiple variables, and has linear time and space complexity, making it highly scalable. Experimental results on synthetic and real-world datasets demonstrate the superior performance of our approach compared to state-of-the-art GP approximations in terms of both time and accuracy.
Article
Computer Science, Artificial Intelligence
Enrique Miranda, Marco Zaffalon
Summary: Desirability is an extension of Bayesian decision theory to sets of expected utilities, incorporating a linear assumption in measuring rewards. However, this assumption contradicts a general representation of rational decision making, as shown by the Allais paradox. By representing the utility scale via a general closure operator, desirability can be extended to the nonlinear case, allowing for expressing rewards in actual nonlinear currency while minimizing foundational assumptions.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2023)
Article
Computer Science, Artificial Intelligence
Marco Zaffalon, Alessandro Antonucci, Rafael Cabanas, David Huber
Summary: This paper addresses the integration of data from multiple observational and interventional studies, which may be biased, in order to compute counterfactuals in structural causal models. The paper proposes a causal expectation-maximization scheme to approximate the bounds for partially identifiable counterfactual queries. Additionally, the paper demonstrates how this approach can be extended to handle multiple datasets, regardless of their type or bias, by using graphical transformations. The effectiveness of the proposed approach is validated through numerical experiments and a case study on palliative care, indicating the benefits of fusing heterogeneous data sources in the presence of partial identifiability.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2023)
Proceedings Paper
Automation & Control Systems
Franca Corradini, Francesco Flammini, Alessandro Antonucci
Summary: In this paper, the potential of probabilistic modelling approaches for ensuring trustworthy AI in drone-supported autonomous wheelchairs' sensing subsystems is addressed. Probabilistic models can capture uncertainty and nonstationarity in the environment and sensory system, enabling informed decisions and safe autonomy. The approach is being developed in a European project named REXASI-PRO, which focuses on modelling methodology, tools, reference architecture, design, and implementation guidelines. Different use cases are considered to demonstrate the effectiveness of the proposed approach in providing trustworthy autonomous wheelchairs in real-world environments.
FIRST INTERNATIONAL SYMPOSIUM ON TRUSTWORTHY AUTONOMOUS SYSTEMS, TAS 2023
(2022)
Proceedings Paper
Computer Science, Artificial Intelligence
Alberto Termine, Alessandro Antonucci, Alessandro Facchini, Giuseppe Primiero
Summary: Probabilistic model checking is crucial for computational systems with stochastic nature. Imprecise probabilities and imprecise Markov reward models provide a robust approach to overcome limitations in standard probabilistic model checking by considering uncertainty and sensitivity analysis. Efficient algorithms for computing lower and upper bounds of expected rewards in real-world cases have been developed based on these concepts.
PROCEEDINGS OF THE TWELVETH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS
(2021)
Proceedings Paper
Computer Science, Artificial Intelligence
Marco Zaffalon, Enrique Miranda
Summary: The sure-thing principle states that if action a is preferred to action b under an event and its complement, then a should be preferred over b. Despite its intuitive nature, it is not a logical principle and may fail in certain contexts due to deeper concepts in causality, decision theory, and probability. In non-causal settings, it follows from considerations of temporal coherence and rationality, while in causal settings, it can be derived using coherence and a causal independence condition.
PROCEEDINGS OF THE TWELVETH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS
(2021)
Proceedings Paper
Computer Science, Artificial Intelligence
Alessio Benavoli, Alessandro Facchini, Marco Zaffalon
Summary: Understanding systems of identical particles requires the symmetrization postulate and updating exchangeable observables through exchangeability assessments. Quantum mechanics can be seen as a normative and algorithmic theory that guides an agent to assess their subjective beliefs.
PROCEEDINGS OF THE TWELVETH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS
(2021)
Proceedings Paper
Computer Science, Artificial Intelligence
Rafael Cabanas, Alessandro Antonucci
Summary: The paper introduces a Java library called CREMA for modeling, processing, and querying credal networks. Despite the NP-hardness of exact credal network inferences, there are many approximate algorithms available. CREPO is an open repository that provides synthetic credal networks and the exact results of inference tasks on these models.
PROCEEDINGS OF THE TWELVETH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS
(2021)
Article
Computer Science, Artificial Intelligence
Timotheus Kampik, Kristijonas Cyras, Jose Ruiz Alarcon
Summary: This paper presents a formal approach to explaining changes in inference in Quantitative Bipolar Argumentation Frameworks (QBAFs). The approach traces the causes of strength inconsistencies and provides explanations for them.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2024)
Article
Computer Science, Artificial Intelligence
Xiangnan Zhou, Longchun Wang, Qingguo Li
Summary: This paper aims to establish a closer connection between domain theory and Formal Concept Analysis (FCA) by introducing the concept of an optimized concept for a formal context. With the utilization of optimized concepts, it is demonstrated that the class of formal contexts directly corresponds to algebraic domains. Additionally, two subclasses of formal contexts are identified to characterize algebraic L-domains and Scott domains. An application is presented to address the open problem of reconstructing bounded complete continuous domains using attribute continuous contexts, and the presentation of algebraic domains is extended to a categorical equivalence.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2024)
Article
Computer Science, Artificial Intelligence
Sihan Wang, Zhong Yuan, Chuan Luo, Hongmei Chen, Dezhong Peng
Summary: Anomaly detection is widely used in various fields, but most current methods only work for specific data and ignore uncertain information such as fuzziness. This paper proposes an anomaly detection algorithm based on fuzzy rough entropy, which effectively addresses the similarity between high-dimensional objects using distance and correlation measures. The algorithm is compared and analyzed with mainstream anomaly detection algorithms on publicly available datasets, showing superior performance and flexibility.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2024)
Article
Computer Science, Artificial Intelligence
Mario Alviano, Francesco Bartoli, Marco Botta, Roberto Esposito, Laura Giordano, Daniele Theseider Dupre
Summary: This paper investigates the relationships between a multipreferential semantics in defeasible reasoning and a multilayer neural network model. Weighted knowledge bases are considered for a simple description logic with typicality under a concept-wise multipreference semantics. The semantics is used to interpret MultiLayer Perceptrons (MLPs) preferentially. Model checking and entailment based approach are employed in verifying conditional properties of MLPs.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2024)
Article
Computer Science, Artificial Intelligence
Bazin Alexandre, Galasso Jessie, Kahn Giacomo
Summary: Formal concept analysis is a mathematical framework that represents the information in binary object-attribute datasets using a lattice of formal concepts. It has been extended to handle more complex data types, such as relational data and n-ary relations. This paper presents a framework for polyadic relational concept analysis, which extends relational concept analysis to handle relational datasets consisting of n-ary relations.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2024)
Article
Computer Science, Artificial Intelligence
Ander Gray, Marcelo Forets, Christian Schilling, Scott Ferson, Luis Benet
Summary: The presented method combines reachability analysis and probability bounds analysis to handle imprecisely known random variables. It can rigorously compute the temporal evolution of p-boxes and provide interval probabilities for formal verification problems. The method does not impose strict constraints on the input probability distribution or p-box and can handle multivariate p-boxes with a consonant approximation method.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2024)
Article
Computer Science, Artificial Intelligence
Laszlo Csato
Summary: This paper studies a special type of incomplete pairwise comparison matrices and proposes a new method to determine the missing elements without violating the ordinal property.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2024)
