This paper presents the Min-Cut Bayesian Network Consensus (MCBNC) algorithm, a greedy method for structural consensus of Bayesian Networks (BNs), with applications in federated learning and model aggregation. MCBNC prunes weak edges from an initial unrestricted fusion using a structural score based on min-cut analysis, integrated into a modified Backward Equivalence Search (BES) phase of the Greedy Equivalence Search (GES) algorithm. The score quantifies edge support across input networks and is computed using max-flow. Unlike methods with fixed treewidth bounds, MCBNC introduces a pruning threshold θ that can be selected post hoc using only structural information. Experiments on real-world BNs show that MCBNC yields sparser, more accurate consensus structures than both canonical fusion and the input networks. The method is scalable, data-agnostic, and well-suited for distributed or federated structural learning of BNs or causal discovery.

A multivalued network on a complement-closed set (MCN) is a dynamical network model whose entities can take multiple state values in a totally ordered set equipped with a complement operator. Multivalued networks extend the framework of standard (binary) Boolean networks and several types of multivalued network models. In this work, we study steady states in MCN where an undirected graph, in which the entities may or may not have self-loops, encodes the dependencies in the network, and all the local functions are maximum (respectively minimum)- type. Specifically, we give a necessary and sufficient condition for the existence of steady states and provide a complete structural description of them. Additionally, we completely characterize when the steady states of MCN cannot be directly obtained from those of its binary counterpart. In doing so, we show that a Fixed Point Theorem does not hold for these systems, when they are non-binary. Moreover, this result extends to broader classes of MCN in which more general independent local functions are considered.

Bayesian Network (BN) fusion combines multiple input networks into a single structure, balancing dependency preservation with computational tractability. While unrestricted fusion retains all dependencies, it often results in overly complex networks with high treewidth, which affects inference scalability. Limited fusion mitigates this by pruning edges to control treewidth but risks overfitting to input-specific noise and omitting dependencies from the original BNs. This paper introduces a consensus framework that prioritizes shared structures among input networks while enforcing treewidth constraints, ensuring a good consensus. We propose genetic algorithms with advanced initialization, specialized operators, and a tailored fitness function. Additionally, we adapt existing methods to this problem and implement greedy baselines for benchmarking and further optimization. Experiments on synthetic and real-world BNs show the superiority of the proposed genetic algorithms over the adapted methods and greedy baselines.

Abstract Ensemble of label ranking trees (LRTs) are currently the state‐of‐the‐art approaches to the label ranking problem. Recently, bagging, boosting, and random forest methods have been proposed, all based on the LRT algorithm, which adapts regression/classification trees to the label classification problem. The LRT algorithm uses theoretically grounded Mallows probability distribution to select the best split when growing the tree, and an EM‐type process to complete the rankings on the training data when they are incomplete. These two steps have proven to be accurate, but require a large computational effort. This article proposes two alternative methods that replace the use of the Mallows distribution with distance‐based criteria to select the best split at each inner node of the tree. Moreover, these distance‐based criteria allow dealing with incomplete rankings natively, so avoiding the completion process. We have carried out an extensive experimental evaluation, which shows that (1) the integration of the two proposed modifications to the LRT algorithm into ensemble methods (bagging and random forest) are an order of magnitude faster than using the original Mallows‐based LRT algorithm; (2) ensembles using the proposed LRT methods are significantly more accurate in the presence of incomplete rankings, while they are at least as accurate in the complete case; and (3) the two modified LRT algorithms are also an order of magnitude faster than the Mallows‐based LRT, while they are at least as accurate as the Mallows‐based LRT on both complete and incomplete rankings.

Label ranking studies the problem of learning a preference model that maps instances to rankings over a finite set of predefined class labels. The training data used to solve this problem consists of instances labeled with rankings. Since these rankings are often incomplete, models need to be able to deal with missing information in the class labels to be more useful in practice. Several decision tree models have been proposed to learn from incomplete rankings, mainly using axis-parallel decision nodes, which is the standard approach for decision tree induction. In contrast to this strategy, this present work introduces a method for learning oblique decision trees for the label ranking problem, as they have been shown to improve performance in the standard classification scenario. Our experimentation shows that this method offers several advantages over the current decision tree model. Not only does it generate more compact tree structures, but it is also shown to achieve outstandingly better results for complete rankings and in cases with a low percentage of missing labels. Moreover, the proposed method is faster in the largest datasets than the current decision tree model.

The label ranking problem consists in learning preference models from training datasets labeled with (possibly incomplete) rankings of the class labels. The goal is then to predict a ranking for a given unlabeled instance. This work focuses on a more general interpretation where both the training dataset and the prediction given as output allow tied class labels, i.e., there is no particular preference between them. This problem is known as the partial label ranking problem. This paper tackles the partial label ranking problem by transforming the ranking with ties into a set of discrete variables representing the preference relations (ranked ahead, tied with, and ranked behind) between each pair of class labels. The posterior probabilities for each pair are then used to fill the values of a preference matrix. This preference matrix is the basis for solving the rank aggregation problem required to obtain the output ranking with ties. This paper aims to exploit the resemblance of this problem with multi-label and multi-dimensional classification by studying the use of Bayesian network classifiers to compute the posterior probabilities for the new class structure, i.e., pairs of class labels. In particular, binary relevance with naive Bayes and averaged one-dependence estimators between the new class structure are used to solve the partial label ranking problem. Furthermore, bivariate relationships between all the pairs of class labels are considered. However, the complexity of the model grows significantly, which makes it necessary to reduce the number of allowed bivariate relationships between pairs. Thus, a feature selection method is included to select the more relevant subset of bivariate relationships. The experimental evaluation shows that our proposals are competitive in accuracy with the current instance-based and decision tree induction algorithms. Moreover, they outperform the existing mixture-based probabilistic graphical models, while the algorithms proposed are much faster.

In this work, we provide a procedure that allows us to transform certain kinds of deterministic Boolean networks on minterm or maxterm functions into symmetric ones, so inferring that such symmetrizable networks can present only periodic points of periods 1 or 2. In particular, we deal with generalized parallel (or synchronous) dynamical systems (GPDS) over undirected graphs, i.e., discrete parallel dynamical systems over undirected graphs where some of the self-loops may not appear. We also study the class of anti-symmetric GPDS (which are non-symmetrizable), proving that their periodic orbits have period 4. In addition, we introduce a class of non-symmetrizable systems which admit periodic orbits with arbitrary large periods.

The partial label ranking problem is a particular preference learning scenario that focuses on learning preference models from data, such that they predict a complete ranking with ties defined over the values of the class variable for a given input instance. This work proposes to transform the rankings into preference relations among pairs of class labels and to learn a standard classifier for each of them. This classifier is then used to estimate the probability of each event from the preference relation between the two compared class labels. Finally, the probabilities obtained for each preference comparison are used to compute a preference matrix utilized to solve the corresponding rank aggregation problem and so obtain the ranking among all the class labels. The experimental evaluation shows that the proposed method is ranked ahead of competing algorithms in accuracy while obtaining similar CPU time results.

Classification algorithms have recently acquired great popularity due to their efficiency to generate models capable of solving high complexity problems. Specifically, black box models are the ones that offer the best results, since they greatly benefit from the enormous amount of data available to learn models in an increasingly accurate way. However, their main disadvantage compared to other simpler algorithms, e.g., decision trees, is the loss of interpretability for both the model and the individual classifications, which may become a major drawback because of the increasing number of applications where it is advisable and even compulsory to provide an explanation. A well-accepted practice is to build anexplainablemodel that can mimic the behavior of the (more complex) classifier in the neighborhood of the instance to be explained. Nonetheless, the generation of explanations in such white box models is not trivial either, which has generated intense research. It is common to generate two types of explanations, factual explanations and counterfactual explanations, which complement each other to justify why the instance has been classified into a certain class or category. In this work, we propose the definition of factual and counterfactual explanations in the frame of fuzzy decision trees, where multiple branches can be fired at once. Our proposal is centered around the definition of factual explanations that can contain more than a single rule, in contrast to the current standard that is limited to considering a single rule as a factual explanation. Moreover, we introduce the idea ofrobustfactual explanation. Finally, we provide procedures to obtain counterfactual explanations from the instance and also from a factual explanation.

The Label Ranking (LR) problem is a well-known nonstandard supervised classification problem, the goal of which is to learn preference classifiers from data, mapping instances to rankings of the labels of the class variable. In the literature, the particular setting where the output of the LR problem is a complete ranking without ties (a.k.a. permutation) has been profusely studied, and many algorithms have been designed to solve these particular instances based on the use of specific probability distributions and aggregation methods for permutations. However, also partial orders (a.k.a. bucket orders) can be considered as output in LR problems (i.e., some labels of the class variable may be tied), but the algorithms available do not tackle this kind of ranking. We refer to this particular case of LR as the Partial Label Ranking (PLR) problem. Thus, motivated by the lack of current methods to deal with the PLR problem, we design machine learning algorithms based on instance-based and decision tree approaches to tackle the PLR problem. We evaluate our proposals on a benchmark of 15 data sets obtained by transforming multiclass instances, and analyze their performance by carrying out a standard machine learning statistical analysis procedure.

The Optimal Bucket Order Problem (OBOP) is a rank aggregation problem which consists in finding a consensus ranking (with ties) that generalizes a set of input rankings. In this paper, with the aim of solving the OBOP in an efficient and scalable way, we propose several greedy algorithms based on different sort-first and cluster-second strategies. More specifically, the sorting step is based on the Borda method, whereas in the cluster step, pairs of adjacent buckets are suitably joined. The proposed methods are experimentally compared with the state-of-the-art greedy algorithms for solving the OBOP by using a large benchmark of real-world databases. Furthermore, we provide a complete statistical analysis of the experimental study, which shows that several of the proposed algorithms outperform the current state-of-the-art greedy algorithms. We also analyze the trade-off between accuracy and execution time of the algorithms to guide the users regarding the selection of the best option for each particular case. The study carried out shows that our proposal is not only competitive in terms of accuracy with the state-of-the-art evolutionary strategy for dealing with the OBOP, but is also fast and scalable.

As the data sets increase in size, the process of manually labeling data becomes unfeasible by small groups of experts. Thus, it is common to rely on crowdsourcing platforms which provide inexpensive, but noisy, labels. Although implementations of algorithms to tackle this problem exist, none of them focus on scalability, limiting the area of application to relatively small data sets. In this paper, we present spark-crowd, an Apache Spark package for learning from crowdsourced data with scalability in mind.

Annual journal rankings are usually considered a tool for the evaluation of research and researchers. Although they are an objective resource for such evaluation, they also present drawbacks: (a) the uncertainty about the definite position of a target journal in the corresponding annual ranking when selecting a journal, and (b) in spite of the nonsignificant difference in score (for instance, impact factor) between consecutive journals in the ranking, the journals are strictly ranked and eventually placed in different terciles/quartiles, which may have a significant influence in the subsequent evaluation. In this article we present several proposals to obtain an aggregated consensus ranking as an alternative/complementary tool to standardize annual rankings. To illustrate the proposed methodology we use as a case study the Journal Citation Reports, and in particular the category of Computer Science: Artificial Intelligence (CS:AI). In the context of the consensus rankings obtained by the different methods, we discuss the convenience of using one or the other procedure according to the corresponding framework. In particular, our proposals allow us to obtain consensus rankings that avoid crisp frontiers between similarly ranked journals and consider the longitudinal/temporal evolution of the journals.