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Special Issue on Mathematics in Artificial Intelligence

    Paola Galdi and Jacques Fleuriot are editing a special issue of the journal Mathematics in Computer Science focused on the interplay between mathematics and AI. The Call for Papers can be found here. The submission deadline is on the 31st of January 2024.


    Paper on conformance checking over probabilistic events accepted at HICSS-57

      The paper on “Alignment-based conformance checking over probabilistic events” by Jiawei Zheng, Petros Papapanagiotou and Jacques Fleuriot has been accepted at the Hawaii International Conference on System Sciences (HICSS-57).


      Conformance checking techniques allow us to evaluate how well some exhibited behaviour, represented by a trace of monitored events, conforms to a specified process model. Modern monitoring and activity recognition technologies, such as those relying on sensors, the IoT, statistics and AI, can produce a wealth of relevant event data. However, this data is typically characterised by noise and uncertainty, in contrast to the assumption of a deterministic event log required by conformance checking algorithms. In this paper, we extend alignment-based conformance checking to function under a probabilistic event log.

      We introduce a weighted trace model and weighted alignment cost function, and a custom threshold parameter that controls the level of confidence on the event data vs. the process model. The resulting algorithm considers activities of lower but sufficiently high probability that better align with the process model. We explain the algorithm and its motivation both from formal and intuitive perspectives, and demonstrate its functionality in comparison with deterministic alignment using real-life datasets.

      Keywords: Conformance checking, Probabilistic events, Uncertainty, Probabilistic cost function

      Pre-print on Associations between Morbidities in Small But Important Subgroup using a Bayesian approach

        Our paper on the “Associations between Morbidities in Small But Important Subgroups: A Novel Bayesian Approach for Robust Multimorbidity Analysis with Small Sample Sizes”  is out.


        Background: Robustly examining associations between long-term conditions may be important in identifying opportunities for intervention in multimorbidity but is challenging when data is limited. We have developed a Bayesian inference framework that is robust to sparse data and have used it to quantify morbidity associations in the oldest old, a population with limited available data.

        Methods: We conducted a retrospective cross-sectional cohort study of a representative dataset of primary care patients in Scotland. We included 40 long-term conditions and studied their associations in 12,009 individuals aged 90 and older, stratified by sex, to study the effect of small sample sizes in the estimation of associations between long-term conditions. We analysed associations obtained with Relative Risk (RR), a standard measure in the literature, and compared them with a new measure of associations, Associations Beyond Chance (ABC), that utilises a Bayesian framework. To enable a broad exploration of interactions between long-term conditions, we built networks of association and assessed differences in their analysis when associations are estimated by RR or ABC.

        Findings: Our Bayesian framework was appropriately more cautious in attributing association when evidence is small, as it dismissed six of the top ten associations reported by RR, most of which relate to uncommon conditions. This caution in reporting association was also present in reporting differences in associations between sex, for which ABC only reported as significant about one-fifth of those reported by RR. Last, the presence of potentially inaccurate associations by RR also affected the aggregated measures of multimorbidity and network representations.

        Interpretation: Incorporating uncertainty into multimorbidity research is crucial to avoid misleading findings when data is limited, a problem that particularly affects small but important subgroups. Our proposed framework improves the reliability of estimations of associations and, more in general, of research into disease mechanisms and multimorbidity.

        More information at SSRN: or

        Paper on brain tumour survival predictions accepted in Computer Methods and Programs in Biomedicine

          Our paper on the “Development of prediction models for one-year brain tumour survival using machine learning: a comparison of accuracy and interpretability” has been published in Computer Methods and Programs in Biomedicine. The work by Colleen Charlton, Michael Poon, Paul Brennan and Jacques Fleuriot looks at classification models for predicting brain tumour survival over one year, with an emphasis on interpretable/Explainable AI.  The paper can be accessed here.

          Survey pre-print on Neurosymbolic AI for Reasoning on Graph Structures is out on arXiv

            Our article on Neurosymbolic AI for Reasoning on Graph Structure is out. This is a comprehensive survey by Lauren Nicole DeLong, Ramon Fernández Mir, Matthew Whyte, Zonglin Ji and Jacques D. Fleuriot.


            Neurosymbolic AI is an increasingly active area of research which aims to combine symbolic reasoning methods with deep learning to generate models with both high predictive performance and some degree of human-level comprehensibility. As knowledge graphs are becoming a popular way to represent heterogeneous and multi-relational data, methods for reasoning on graph structures have attempted to follow this neurosymbolic paradigm. Traditionally, such approaches have utilized either rule-based inference or generated representative numerical embeddings from which patterns could be extracted. However, several recent studies have attempted to bridge this dichotomy in ways that facilitate interpretability, maintain performance, and integrate expert knowledge. Within this article, we survey a breadth of methods that perform neurosymbolic reasoning tasks on graph structures. Within this article, we survey a breadth of methods that perform neurosymbolic reasoning tasks on graph structures. To better compare the various methods, we propose a novel taxonomy by which we can classify them. Specifically, we propose three major categories: (1) logically-informed embedding approaches, (2) embedding approaches with logical constraints, and (3) rule-learning approaches. Alongside the taxonomy, we provide a tabular overview of the approaches and links to their source code, if available, for more direct comparison. Finally, we discuss the applications on which these methods were primarily used and propose several prospective directions toward which this new field of research could evolve.

            The paper can be found on arXiv at arXiv:2302.07200 and an associated Github repository is here.