Alessandro Antonucci

Marco Zaffalon, Alessandro Antonucci, Rafael Cabañas et al.

We address the problem of integrating data from multiple, possibly biased, observational and interventional studies, to eventually compute counterfactuals in structural causal models. We start from the case of a single observational dataset affected by a selection bias. We show that the likelihood of the available data has no local maxima. This enables us to use the causal expectation-maximisation scheme to approximate the bounds for partially identifiable counterfactual queries, which are the focus of this paper. We then show how the same approach can address the general case of multiple datasets, no matter whether interventional or observational, biased or unbiased, by remapping it into the former one via graphical transformations. Systematic numerical experiments and a case study on palliative care show the effectiveness of our approach, while hinting at the benefits of fusing heterogeneous data sources to get informative outcomes in case of partial identifiability.

Marco Zaffalon, Alessandro Antonucci, Rafael Cabañas et al.

We assume to be given structural equations over discrete variables inducing a directed acyclic graph, namely, a structural causal model, together with data about its internal nodes. The question we want to answer is how we can compute bounds for partially identifiable counterfactual queries from such an input. We start by giving a map from structural casual models to credal networks. This allows us to compute exact counterfactual bounds via algorithms for credal nets on a subclass of structural causal models. Exact computation is going to be inefficient in general given that, as we show, causal inference is NP-hard even on polytrees. We target then approximate bounds via a causal EM scheme. We evaluate their accuracy by providing credible intervals on the quality of the approximation; we show through a synthetic benchmark that the EM scheme delivers accurate results in a fair number of runs. In the course of the discussion, we also point out what seems to be a neglected limitation to the trending idea that counterfactual bounds can be computed without knowledge of the structural equations. We also present a real case study on palliative care to show how our algorithms can readily be used for practical purposes.

Marco Zaffalon, Alessandro Antonucci, Rafael Cabañas et al.

Causal analysis may be affected by selection bias, which is defined as the systematic exclusion of data from a certain subpopulation. Previous work in this area focused on the derivation of identifiability conditions. We propose instead a first algorithm to address both identifiable and unidentifiable queries. We prove that, in spite of the missingness induced by the selection bias, the likelihood of the available data is unimodal. This enables us to use the causal expectation-maximisation scheme to obtain the values of causal queries in the identifiable case, and to compute bounds otherwise. Experiments demonstrate the approach to be practically viable. Theoretical convergence characterisations are provided.

David Huber, Yizuo Chen, Alessandro Antonucci et al.

We discuss the problem of bounding partially identifiable queries, such as counterfactuals, in Pearlian structural causal models. A recently proposed iterated EM scheme yields an inner approximation of those bounds by sampling the initialisation parameters. Such a method requires multiple (Bayesian network) queries over models sharing the same structural equations and topology, but different exogenous probabilities. This setup makes a compilation of the underlying model to an arithmetic circuit advantageous, thus inducing a sizeable inferential speed-up. We show how a single symbolic knowledge compilation allows us to obtain the circuit structure with symbolic parameters to be replaced by their actual values when computing the different queries. We also discuss parallelisation techniques to further speed up the bound computation. Experiments against standard Bayesian network inference show clear computational advantages with up to an order of magnitude of speed-up.

Ardian Selmonaj, Oleg Szehr, Giacomo Del Rio et al.

The application of artificial intelligence to simulate air-to-air combat scenarios is attracting increasing attention. To date the high-dimensional state and action spaces, the high complexity of situation information (such as imperfect and filtered information, stochasticity, incomplete knowledge about mission targets) and the nonlinear flight dynamics pose significant challenges for accurate air combat decision-making. These challenges are exacerbated when multiple heterogeneous agents are involved. We propose a hierarchical multi-agent reinforcement learning framework for air-to-air combat with multiple heterogeneous agents. In our framework, the decision-making process is divided into two stages of abstraction, where heterogeneous low-level policies control the action of individual units, and a high-level commander policy issues macro commands given the overall mission targets. Low-level policies are trained for accurate unit combat control. Their training is organized in a learning curriculum with increasingly complex training scenarios and league-based self-play. The commander policy is trained on mission targets given pre-trained low-level policies. The empirical validation advocates the advantages of our design choices.

Alessandro Antonucci, Francesca Mangili, Claudio Bonesana et al.

Directed graphical models such as Bayesian nets are often used to implement intelligent tutoring systems able to interact in real-time with learners in a purely automatic way. When coping with such models, keeping a bound on the number of parameters might be important for multiple reasons. First, as these models are typically based on expert knowledge, a huge number of parameters to elicit might discourage practitioners from adopting them. Moreover, the number of model parameters affects the complexity of the inferences, while a fast computation of the queries is needed for real-time feedback. We advocate logical gates with uncertainty for a compact parametrization of the conditional probability tables in the underlying Bayesian net used by tutoring systems. We discuss the semantics of the model parameters to elicit and the assumptions required to apply such approach in this domain. We also derive a dedicated inference scheme to speed up computations.

Francesca Mangili, Giorgia Adorni, Alberto Piatti et al.

Automatic assessment of learner competencies is a fundamental task in intelligent tutoring systems. An assessment rubric typically and effectively describes relevant competencies and competence levels. This paper presents an approach to deriving a learner model directly from an assessment rubric defining some (partial) ordering of competence levels. The model is based on Bayesian networks and exploits logical gates with uncertainty (often referred to as noisy gates) to reduce the number of parameters of the model, so to simplify their elicitation by experts and allow real-time inference in intelligent tutoring systems. We illustrate how the approach can be applied to automatize the human assessment of an activity developed for testing computational thinking skills. The simple elicitation of the model starting from the assessment rubric opens up the possibility of quickly automating the assessment of several tasks, making them more easily exploitable in the context of adaptive assessment tools and intelligent tutoring systems.

Giorgia Adorni, Francesca Mangili, Alberto Piatti et al.

In modern and personalised education, there is a growing interest in developing learners' competencies and accurately assessing them. In a previous work, we proposed a procedure for deriving a learner model for automatic skill assessment from a task-specific competence rubric, thus simplifying the implementation of automated assessment tools. The previous approach, however, suffered two main limitations: (i) the ordering between competencies defined by the assessment rubric was only indirectly modelled; (ii) supplementary skills, not under assessment but necessary for accomplishing the task, were not included in the model. In this work, we address issue (i) by introducing dummy observed nodes, strictly enforcing the skills ordering without changing the network's structure. In contrast, for point (ii), we design a network with two layers of gates, one performing disjunctive operations by noisy-OR gates and the other conjunctive operations through logical ANDs. Such changes improve the model outcomes' coherence and the modelling tool's flexibility without compromising the model's compact parametrisation, interpretability and simple experts' elicitation. We used this approach to develop a learner model for Computational Thinking (CT) skills assessment. The CT-cube skills assessment framework and the Cross Array Task (CAT) are used to exemplify it and demonstrate its feasibility.

Marco Zaffalon, Alessandro Antonucci, David Huber et al.

We address the problem of integrating data from multiple, possibly biased, observational and interventional studies, to eventually compute counterfactuals in structural causal models. We start from the case of a single observational dataset affected by a selection bias. We show that the likelihood of the available data has no local maxima. This enables us to use the causal expectation-maximisation scheme to compute approximate bounds for partially identifiable counterfactual queries, which are the focus of this paper. We then show how the same approach can solve the general case of multiple datasets, no matter whether interventional or observational, biased or unbiased, by remapping it into the former one via graphical transformations. Systematic numerical experiments and a case study on palliative care show the effectiveness and accuracy of our approach, while hinting at the benefits of integrating heterogeneous data to get informative bounds in case of partial identifiability.

Adrian Cosma, Oleg Szehr, David Kletz et al.

Feature extraction from unstructured text is a critical step in many downstream classification pipelines, yet current approaches largely rely on hand-crafted prompts or fixed feature schemas. We formulate feature discovery as a dataset-level prompt optimization problem: given a labelled text corpus, the goal is to induce a global set of interpretable and discriminative feature definitions whose realizations optimize a downstream supervised learning objective. To this end, we propose a multi-agent prompt optimization framework in which language-model agents jointly propose feature definitions, extract feature values, and evaluate feature quality using dataset-level performance and interpretability feedback. Instruction prompts are iteratively refined based on this structured feedback, enabling optimization over prompts that induce shared feature sets rather than per-example predictions. This formulation departs from prior prompt optimization methods that rely on per-sample supervision and provides a principled mechanism for automatic feature discovery from unstructured text.

Alessandro Antonucci, Gregorio Piqué, Marco Zaffalon

We evaluate the ability of large language models (LLMs) to infer causal relations from natural language. Compared to traditional natural language processing and deep learning techniques, LLMs show competitive performance in a benchmark of pairwise relations without needing (explicit) training samples. This motivates us to extend our approach to extrapolating causal graphs through iterated pairwise queries. We perform a preliminary analysis on a benchmark of biomedical abstracts with ground-truth causal graphs validated by experts. The results are promising and support the adoption of LLMs for such a crucial step in causal inference, especially in medical domains, where the amount of scientific text to analyse might be huge, and the causal statements are often implicit.

Alessia Berarducci, Eric Rossetto, Alessandro Antonucci et al.

AutoML, intended as the process of automating the application of machine learning to real-world problems, is a key step for AI popularisation. Most AutoML frameworks are not accounting for the potential lack of fairness in the training data and in the corresponding predictions. We introduce \textsc{FairMind}, a software prototype aiming to automatise fairness analysis at the dataset level. We achieve that by resorting to the assumptions of the \emph{standard fairness model}, recently proposed by Plečko and Bareinboim. This allows for a sound fairness evaluation in terms of causal effects, based on \emph{counterfactual} queries involving the target, possibly confounders and mediators, and the different values of an input feature we regard as \emph{protected}. After the necessary data preprocessing, the tool implements a closed-form computation of the effects. LLMs are consequently exploited to generate accurate reports on the fairness levels detected in the training dataset. We achieve that in a zero-shot setup and show by examples the expected advantages with respect to a direct analysis performed by the LLM. To favour applications, extensions to ordinal protected variable and continuous targets and novel decomposition results are also discussed.

Carlo Grigioni, Franca Corradini, Alessandro Antonucci et al.

Safe road-crossing by self-driving vehicles is a crucial problem to address in smart-cities. In this paper, we introduce a multi-sensor fusion approach to support road-crossing decisions in a system composed by an autonomous wheelchair and a flying drone featuring a robust sensory system made of diverse and redundant components. To that aim, we designed an analytical danger function based on explainable physical conditions evaluated by single sensors, including those using machine learning and artificial vision. As a proof-of-concept, we provide an experimental evaluation in a laboratory environment, showing the advantages of using multiple sensors, which can improve decision accuracy and effectively support safety assessment. We made the dataset available to the scientific community for further experimentation. The work has been developed in the context of an European project named REXASI-PRO, which aims to develop trustworthy artificial intelligence for social navigation of people with reduced mobility.

Ardian Selmonaj, Giacomo Del Rio, Adrian Schneider et al.

Achieving mission objectives in a realistic simulation of aerial combat is highly challenging due to imperfect situational awareness and nonlinear flight dynamics. In this work, we introduce a novel 3D multi-agent air combat environment and a Hierarchical Multi-Agent Reinforcement Learning framework to tackle these challenges. Our approach combines heterogeneous agent dynamics, curriculum learning, league-play, and a newly adapted training algorithm. To this end, the decision-making process is organized into two abstraction levels: low-level policies learn precise control maneuvers, while high-level policies issue tactical commands based on mission objectives. Empirical results show that our hierarchical approach improves both learning efficiency and combat performance in complex dogfight scenarios.

Ardian Selmonaj, Giacomo Del Rio, Adrian Schneider et al.

We present a system that enables real-time interaction between human users and agents trained to control fighter jets in simulated 3D air combat scenarios. The agents are trained in a dedicated environment using Multi-Agent Reinforcement Learning. A communication link is developed to allow seamless deployment of trained agents into VR-Forces, a widely used defense simulation tool for realistic tactical scenarios. This integration allows mixed simulations where human-controlled entities engage with intelligent agents exhibiting distinct combat behaviors. Our interaction model creates new opportunities for human-agent teaming, immersive training, and the exploration of innovative tactics in defense contexts.

Oscar Lithgow-Serrano, Vani Kanjirangat, Alessandro Antonucci

Recent papers show LLMs achieve near-random accuracy in causal relation classification, raising questions about whether such failures arise from limited pretraining exposure or deeper representational gaps. We investigate this under uncertainty-based evaluation, testing whether pretraining exposure to causal examples improves causal understanding >18K PubMed sentences -- half from The Pile corpus, half post-2024 -- across seven models (Pythia-1.4B/7B/12B, GPT-J-6B, Dolly-7B/12B, Qwen-7B). We analyze model behavior through: (i) causal classification, where the model identifies causal relationships in text, and (ii) verbatim memorization probing, where we assess whether the model prefers previously seen causal statements over their paraphrases. Models perform four-way classification (direct/conditional/correlational/no-relationship) and select between originals and their generated paraphrases. Results show almost identical accuracy on seen/unseen sentences (p > 0.05), no memorization bias (24.8% original selection), and output distribution over the possible options is almost flat, with entropic values near the maximum (1.35/1.39), confirming random guessing. Instruction-tuned models show severe miscalibration (Qwen: > 95% confidence, 32.8% accuracy, ECE=0.49). Conditional relations induce highest entropy (+11% vs. direct). These findings suggest that failures in causal understanding arise from the lack of structured causal representation, rather than insufficient exposure to causal examples during pretraining.

Alessandro Antonucci, Eric Rossetto, Ivan Duvnjak

We investigate individual fairness in generative probabilistic classifiers by analysing the robustness of posterior inferences to perturbations in private features. Building on established results in robustness analysis, we hypothesise a correlation between robustness and predictive accuracy, specifically, instances exhibiting greater robustness are more likely to be classified accurately. We empirically assess this hypothesis using a benchmark of fourteen datasets with fairness concerns, employing Bayesian networks as the underlying generative models. To address the computational complexity associated with robustness analysis over multiple private features with Bayesian networks, we reformulate the problem as a most probable explanation task in an auxiliary Markov random field. Our experiments confirm the hypothesis about the correlation, suggesting novel directions to mitigate the traditional trade-off between fairness and accuracy.

Ardian Selmonaj, Miroslav Strupl, Oleg Szehr et al.

To reliably deploy Multi-Agent Reinforcement Learning (MARL) systems, it is crucial to understand individual agent behaviors. While prior work typically evaluates overall team performance based on explicit reward signals, it is unclear how to infer agent contributions in the absence of any value feedback. In this work, we investigate whether meaningful insights into agent behaviors can be extracted solely by analyzing the policy distribution. Inspired by the phenomenon that intelligent agents tend to pursue convergent instrumental values, we introduce Intended Cooperation Values (ICVs), a method based on information-theoretic Shapley values for quantifying each agent's causal influence on their co-players' instrumental empowerment. Specifically, ICVs measure an agent's action effect on its teammates' policies by assessing their decision (un)certainty and preference alignment. By analyzing action effects on policies and value functions across cooperative and competitive MARL tasks, our method identifies which agent behaviors are beneficial to team success, either by fostering deterministic decisions or by preserving flexibility for future action choices, while also revealing the extent to which agents adopt similar or diverse strategies. Our proposed method offers novel insights into cooperation dynamics and enhances explainability in MARL systems.

Ardian Selmonaj, Oleg Szehr, Giacomo Del Rio et al.

This work presents a Hierarchical Multi-Agent Reinforcement Learning framework for analyzing simulated air combat scenarios involving heterogeneous agents. The objective is to identify effective Courses of Action that lead to mission success within preset simulations, thereby enabling the exploration of real-world defense scenarios at low cost and in a safe-to-fail setting. Applying deep Reinforcement Learning in this context poses specific challenges, such as complex flight dynamics, the exponential size of the state and action spaces in multi-agent systems, and the capability to integrate real-time control of individual units with look-ahead planning. To address these challenges, the decision-making process is split into two levels of abstraction: low-level policies control individual units, while a high-level commander policy issues macro commands aligned with the overall mission targets. This hierarchical structure facilitates the training process by exploiting policy symmetries of individual agents and by separating control from command tasks. The low-level policies are trained for individual combat control in a curriculum of increasing complexity. The high-level commander is then trained on mission targets given pre-trained control policies. The empirical validation confirms the advantages of the proposed framework.

Marco Zaffalon, Alessandro Antonucci

We characterise the likelihood function computed from a Bayesian network with latent variables as root nodes. We show that the marginal distribution over the remaining, manifest, variables also factorises as a Bayesian network, which we call empirical. A dataset of observations of the manifest variables allows us to quantify the parameters of the empirical Bayesian net. We prove that (i) the likelihood of such a dataset from the original Bayesian network is dominated by the global maximum of the likelihood from the empirical one; and that (ii) such a maximum is attained if and only if the parameters of the Bayesian network are consistent with those of the empirical model.

Lilith Mattei, Alessandro Facchini, Alessandro Antonucci

Belief revision is the task of modifying a knowledge base when new information becomes available, while also respecting a number of desirable properties. Classical belief revision schemes have been already specialised to \emph{binary decision diagrams} (BDDs), the classical formalism to compactly represent propositional knowledge. These results also apply to \emph{ordered} BDDs (OBDDs), a special class of BDDs, designed to guarantee canonicity. Yet, those revisions cannot be applied to \emph{sentential decision diagrams} (SDDs), a typically more compact but still canonical class of Boolean circuits, which generalizes OBDDs, while not being a subclass of BDDs. Here we fill this gap by deriving a general revision algorithm for SDDs based on a syntactic characterisation of Dalal revision. A specialised procedure for DNFs is also presented. Preliminary experiments performed with randomly generated knowledge bases show the advantages of directly perform revision within SDD formalism.

Claudio Bonesana, Francesca Mangili, Alessandro Antonucci

We introduce ADAPQUEST, a software tool written in Java for the development of adaptive questionnaires based on Bayesian networks. Adaptiveness is intended here as the dynamical choice of the question sequence on the basis of an evolving model of the skill level of the test taker. Bayesian networks offer a flexible and highly interpretable framework to describe such testing process, especially when coping with multiple skills. ADAPQUEST embeds dedicated elicitation strategies to simplify the elicitation of the questionnaire parameters. An application of this tool for the diagnosis of mental disorders is also discussed together with some implementation details.

Alessandro Antonucci, Alessandro Facchini, Lilith Mattei

Probabilistic sentential decision diagrams are a class of structured-decomposable probabilistic circuits especially designed to embed logical constraints. To adapt the classical LearnSPN scheme to learn the structure of these models, we propose a new scheme based on a partial closed-world assumption: data implicitly provide the logical base of the circuit. Sum nodes are thus learned by recursively clustering batches in the initial data base, while the partitioning of the variables obeys a given input vtree. Preliminary experiments show that the proposed approach might properly fit training data, and generalize well to test data, provided that these remain consistent with the underlying logical base, that is a relaxation of the training data base.

Alessandro Antonucci, Paolo Bevilacqua, Stefano Leonardi et al.

One of the most important barriers toward a widespread use of mobile robots in unstructured and human populated work environments is the ability to plan a safe path. In this paper, we propose to delegate this activity to a human operator that walks in front of the robot marking with her/his footsteps the path to be followed. The implementation of this approach requires a high degree of robustness in locating the specific person to be followed (the leader). We propose a three phase approach to fulfil this goal: 1. identification and tracking of the person in the image space, 2. sensor fusion between camera data and laser sensors, 3. point interpolation with continuous curvature curves. The approach is described in the paper and extensively validated with experimental results.

Alessandro Antonucci, Francesca Mangili, Claudio Bonesana et al.

A test is adaptive when its sequence and number of questions is dynamically tuned on the basis of the estimated skills of the taker. Graphical models, such as Bayesian networks, are used for adaptive tests as they allow to model the uncertainty about the questions and the skills in an explainable fashion, especially when coping with multiple skills. A better elicitation of the uncertainty in the question/skills relations can be achieved by interval probabilities. This turns the model into a credal network, thus making more challenging the inferential complexity of the queries required to select questions. This is especially the case for the information theoretic quantities used as scores to drive the adaptive mechanism. We present an alternative family of scores, based on the mode of the posterior probabilities, and hence easier to explain. This makes considerably simpler the evaluation in the credal case, without significantly affecting the quality of the adaptive process. Numerical tests on synthetic and real-world data are used to support this claim.

Rafael Cabañas, Alessandro Antonucci

Credal networks are a popular class of imprecise probabilistic graphical models obtained as a Bayesian network generalization based on, so-called credal, sets of probability mass functions. A Java library called CREMA has been recently released to model, process and query credal networks. Despite the NP-hardness of the (exact) task, a number of algorithms is available to approximate credal network inferences. In this paper we present CREPO, an open repository of synthetic credal networks, provided together with the exact results of inference tasks on these models. A Python tool is also delivered to load these data and interact with CREMA, thus making extremely easy to evaluate and compare existing and novel inference algorithms. To demonstrate such benchmarking scheme, we propose an approximate heuristic to be used inside variable elimination schemes to keep a bound on the maximum number of vertices generated during the combination step. A CREPO-based validation against approximate procedures based on linearization and exact techniques performed in CREMA is finally discussed.

Simone Mellace, K Vani, Alessandro Antonucci

When coping with literary texts such as novels or short stories, the extraction of structured information in the form of a knowledge graph might be hindered by the huge number of possible relations between the entities corresponding to the characters in the novel and the consequent hurdles in gathering supervised information about them. Such issue is addressed here as an unsupervised task empowered by transformers: relational sentences in the original text are embedded (with SBERT) and clustered in order to merge together semantically similar relations. All the sentences in the same cluster are finally summarized (with BART) and a descriptive label extracted from the summary. Preliminary tests show that such clustering might successfully detect similar relations, and provide a valuable preprocessing for semi-supervised approaches.

Marco Zaffalon, Alessandro Antonucci, Rafael Cabañas

Structural causal models are the basic modelling unit in Pearl's causal theory; in principle they allow us to solve counterfactuals, which are at the top rung of the ladder of causation. But they often contain latent variables that limit their application to special settings. This appears to be a consequence of the fact, proven in this paper, that causal inference is NP-hard even in models characterised by polytree-shaped graphs. To deal with such a hardness, we introduce the causal EM algorithm. Its primary aim is to reconstruct the uncertainty about the latent variables from data about categorical manifest variables. Counterfactual inference is then addressed via standard algorithms for Bayesian networks. The result is a general method to approximately compute counterfactuals, be they identifiable or not (in which case we deliver bounds). We show empirically, as well as by deriving credible intervals, that the approximation we provide becomes accurate in a fair number of EM runs. These results lead us finally to argue that there appears to be an unnoticed limitation to the trending idea that counterfactual bounds can often be computed without knowledge of the structural equations.

K Vani, Sandra Mitrovic, Alessandro Antonucci et al.

Lexical semantic change detection (also known as semantic shift tracing) is a task of identifying words that have changed their meaning over time. Unsupervised semantic shift tracing, focal point of SemEval2020, is particularly challenging. Given the unsupervised setup, in this work, we propose to identify clusters among different occurrences of each target word, considering these as representatives of different word meanings. As such, disagreements in obtained clusters naturally allow to quantify the level of semantic shift per each target word in four target languages. To leverage this idea, clustering is performed on contextualized (BERT-based) embeddings of word occurrences. The obtained results show that our approach performs well both measured separately (per language) and overall, where we surpass all provided SemEval baselines.

Lilith Mattei, Alessandro Antonucci, Denis Deratani Mauá et al.

Probabilistic sentential decision diagrams are logic circuits where the inputs of disjunctive gates are annotated by probability values. They allow for a compact representation of joint probability mass functions defined over sets of Boolean variables, that are also consistent with the logical constraints defined by the circuit. The probabilities in such a model are usually learned from a set of observations. This leads to overconfident and prior-dependent inferences when data are scarce, unreliable or conflicting. In this work, we develop the credal sentential decision diagrams, a generalisation of their probabilistic counterpart that allows for replacing the local probabilities with (so-called credal) sets of mass functions. These models induce a joint credal set over the set of Boolean variables, that sharply assigns probability zero to states inconsistent with the logical constraints. Three inference algorithms are derived for these models, these allow to compute: (i) the lower and upper probabilities of an observation for an arbitrary number of variables; (ii) the lower and upper conditional probabilities for the state of a single variable given an observation; (iii) whether or not all the probabilistic sentential decision diagrams compatible with the credal specification have the same most probable explanation of a given set of variables given an observation of the other variables. These inferences are tractable, as all the three algorithms, based on bottom-up traversal with local linear programming tasks on the disjunctive gates, can be solved in polynomial time with respect to the circuit size. For a first empirical validation, we consider a simple application based on noisy seven-segment display images. The credal models are observed to properly distinguish between easy and hard-to-detect instances and outperform other generative models not able to cope with logical constraints.

Marco Zaffalon, Alessandro Antonucci, Rafael Cabañas

A structural causal model is made of endogenous (manifest) and exogenous (latent) variables. We show that endogenous observations induce linear constraints on the probabilities of the exogenous variables. This allows to exactly map a causal model into a credal network. Causal inferences, such as interventions and counterfactuals, can consequently be obtained by standard algorithms for the updating of credal nets. These natively return sharp values in the identifiable case, while intervals corresponding to the exact bounds are produced for unidentifiable queries. A characterization of the causal models that allow the map above to be compactly derived is given, along with a discussion about the scalability for general models. This contribution should be regarded as a systematic approach to represent structural causal models by credal networks and hence to systematically compute causal inferences. A number of demonstrative examples is presented to clarify our methodology. Extensive experiments show that approximate algorithms for credal networks can immediately be used to do causal inference in real-size problems.

Alessandro Antonucci, Gastone Pietro Rosati Papini, Luigi Palopoli et al.

Generating accurate and efficient predictions for the motion of the humans present in the scene is key to the development of effective motion planning algorithms for robots moving in promiscuous areas, where wrong planning decisions could generate safety hazard or simply make the presence of the robot "socially" unacceptable. Our approach to predict human motion is based on a neural network of a peculiar kind. Contrary to conventional deep neural networks, our network embeds in its structure the popular Social Force Model, a dynamic equation describing the motion in physical terms. This choice allows us to concentrate the learning phase in the aspects, which are really unknown (i.e., the model's parameters) and to keep the structure of the network simple and manageable. As a result, we are able to obtain a good prediction accuracy with a small synthetically generated training set, and the accuracy remains acceptable even when the network is applied in scenarios quite different from those for which it was trained. Finally, the choices of the network are "explainable", as they can be interpreted in physical terms. Comparative and experimental results prove the effectiveness of the proposed approach.

Vani K, Simone Mellace, Alessandro Antonucci

We present two deep learning approaches to narrative text understanding for character relationship modelling. The temporal evolution of these relations is described by dynamic word embeddings, that are designed to learn semantic changes over time. An empirical analysis of the corresponding character trajectories shows that such approaches are effective in depicting dynamic evolution. A supervised learning approach based on the state-of-the-art transformer model BERT is used instead to detect static relations between characters. The empirical validation shows that such events (e.g., two characters belonging to the same family) might be spotted with good accuracy, even when using automatically annotated data. This provides a deeper understanding of narrative plots based on the identification of key facts. Standard clustering techniques are finally used for character de-aliasing, a necessary pre-processing step for both approaches. Overall, deep learning models appear to be suitable for narrative text understanding, while also providing a challenging and unexploited benchmark for general natural language understanding.

Francesca Mangili, Denis Broggini, Alessandro Antonucci et al.

We present a conversational recommendation system based on a Bayesian approach. A probability mass function over the items is updated after any interaction with the user, with information-theoretic criteria optimally shaping the interaction and deciding when the conversation should be terminated and the most probable item consequently recommended. Dedicated elicitation techniques for the prior probabilities of the parameters modeling the interactions are derived from basic structural judgements. Such prior information can be combined with historical data to discriminate items with different recommendation histories. A case study based on the application of this approach to \emph{stagend.com}, an online platform for booking entertainers, is finally discussed together with an empirical analysis showing the advantages in terms of recommendation quality and efficiency.

Alessandro Antonucci, Thomas Tiotto

We present a heuristic strategy for marginal MAP (MMAP) queries in graphical models. The algorithm is based on a reduction of the task to a polynomial number of marginal inference computations. Given an input evidence, the marginals mass functions of the variables to be explained are computed. Marginal information gain is used to decide the variables to be explained first, and their most probable marginal states are consequently moved to the evidence. The sequential iteration of this procedure leads to a MMAP explanation and the minimum information gain obtained during the process can be regarded as a confidence measure for the explanation. Preliminary experiments show that the proposed confidence measure is properly detecting instances for which the algorithm is accurate and, for sufficiently high confidence levels, the algorithm gives the exact solution or an approximation whose Hamming distance from the exact one is small.

Sabina Marchetti, Alessandro Antonucci

We introduce a novel class of adjustment rules for a collection of beliefs. This is an extension of Lewis' imaging to absorb probabilistic evidence in generalized settings. Unlike standard tools for belief revision, our proposal may be used when information is inconsistent with an agent's belief base. We show that the functionals we introduce are based on the imaginary counterpart of probability kinematics for standard belief revision, and prove that, under certain conditions, all standard postulates for belief revision are satisfied.

Sabina Marchetti, Alessandro Antonucci

A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard updating in an augmented credal network, equivalent to a set of consistent Bayesian networks. A characterization of the computational complexity for this task is derived together with an efficient exact procedure for a subclass of instances. In the case of multiple uncertain evidences over the same variable, the proposed procedure can provide a set-valued version of the geometric approach to opinion pooling.

Denis D. Maua, Cassio Polpo de Campos, Alessio Benavoli et al.

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with ternary variables. We prove that under epistemic irrelevance the polynomial time complexity of inferences in credal trees is not likely to extend to more general models (e.g. singly connected networks). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding computational complexity.

Giorgio Corani, Alessandro Antonucci

Bayesian model averaging (BMA) is an approach to average over alternative models; yet, it usually gets excessively concentrated around the single most probable model, therefore achieving only sub-optimal classification performance. The compression-based approach (Boulle, 2007) overcomes this problem, averaging over the different models by applying a logarithmic smoothing over the models' posterior probabilities. This approach has shown excellent performances when applied to ensembles of naive Bayes classifiers. AODE is another ensemble of models with high performance (Webb, 2005), based on a collection of non-naive classifiers (called SPODE) whose probabilistic predictions are aggregated by simple arithmetic mean. Aggregating the SPODEs via BMA rather than by arithmetic mean deteriorates the performance; instead, we aggregate the SPODEs via the compression coefficients and we show that the resulting classifier obtains a slight but consistent improvement over AODE. However, an important issue in any Bayesian ensemble of models is the arbitrariness in the choice of the prior over the models. We address this problem by the paradigm of credal classification, namely by substituting the unique prior with a set of priors. Credal classifier automatically recognize the prior-dependent instances, namely the instances whose most probable class varies, when different priors are considered; in these cases, credal classifiers remain reliable by returning a set of classes rather than a single class. We thus develop the credal version of both the BMA-based and the compression-based ensemble of SPODEs, substituting the single prior over the models by a set of priors. Experiments show that both credal classifiers provide higher classification reliability than their determinate counterparts; moreover the compression-based credal classifier compares favorably to previous credal classifiers.