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.

Image aesthetics assessment (IAA) has been traditionally addressed as a supervised learning problem, where the goal is to accurately predict information related to user opinions, such as the mean opinion score, image ratings, or a binary quality label, usually crafted by using a mean score threshold to label images as highly or lowly aesthetic. Supervised approaches fail to take into account the subjectiveness of this problem, as the idea of aesthetic pleasantness varies among different people and different cultures, thus making the labels extremely noisy. However, the existence of worldwide photographic contests, exhibitions and masters implies that, to a reasonable degree, there is a broader consensus about the quality of very high-quality images and photographs. Furthermore, labelling image data for IAA is a difficult process, as a large amount of non-trivial aesthetic judgements are required for obtaining a large-scale IAA dataset. Therefore, in this work we analyse the potential of positive-unlabelled techniques for solving IAA. We propose techniques for building PU datasets from traditional IAA datasets and from available reference datasets of high-quality images, and test several well-known PU algorithms on these. Our results highlight the potential of PU approaches for IAA, as we obtain results close to the state-of-the-art with much smaller sets of labelled data: in experiments with only 5% of labelled in AVA, we reach accuracy levels only 0.03 points below NIMA, and we reach competent balanced accuracy levels in settings with a very limited amount of labelled data and with very simple models. • We study solving image aesthetic assessment as a positive unlabelled problem. • We make positive unlabelled datasets from known image aesthetic assessment datasets. • We get a balanced accuracy 0.03 points below NIMA with 5% of labelled images in AVA.

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.

We propose ODTE , a new ensemble that uses oblique decision trees as base classifiers. Additionally, we introduce STree, the base algorithm for growing oblique decision trees, which leverages support vector machines to define hyperplanes within the decision nodes. We embed a multiclass strategy (one-vs-one or one-vs-rest) at the decision nodes, allowing the model to directly handle non-binary classification tasks without the need to cluster instances into two groups, as is common in other approaches from the literature. In each decision node, only the best-performing model (SVM)—the one that minimizes an impurity measure for the n-ary classification—is retained, even if the learned SVM addresses a binary classification subtask. An extensive experimental study involving 49 datasets and various state-of-the-art algorithms for oblique decision tree ensembles has been conducted. Our results show that ODTE ranks consistently above its competitors, achieving significant performance gains when hyperparameters are carefully tuned. Moreover, the oblique decision trees learned through STree are more compact than those produced by other algorithms evaluated in our experiments.

This paper introduces an evolutionary computation approach for consensus in structural Bayesian Network (BN) fusion under the constraint of limited treewidth. The consensus BN aims to reconcile multiple input BNs into a single one that retains key structural features present in the original networks. Treewidth, a graph-based parameter associated with computationally tractable inference, is utilized to restrict the complexity of the resulting network. A genetic algorithm is proposed to look for a BN that codifies as much information about the unrestricted fusion as possible while ensuring the treewidth restriction. Experimental evaluation demonstrates the genetic algorithm's ability to obtain consensus BNs with limited treewidth, providing a valuable tool for aggregating information from diverse sources while returning a computationally actionable model.

Learning Bayesian Networks (BNs) from high-dimensional data is a complex and time-consuming task. Although the literature includes approaches based on horizontal (instances) or vertical (variables) partitioning, none can guarantee the same theoretical properties as the Greedy Equivalence Search (GES) algorithm, except those based on the GES algorithm itself. This paper proposes a distributed BN learning algorithm that uses GES as the local learning algorithm, ensuring the same theoretical properties as GES but requiring less CPU time. The two main novelties in our proposed method are (1) the distribution of the set of possible edges among local learning processes, which are constrained to only use its local edge set; and (2) the use of BN fusion to aggregate the networks learned constrained to local edge sets. The algorithm is iterative, and at each step, the last aggregated network is used as the starting point by each local BN process. After a comprehensive experimental evaluation, the results show that the proposed algorithm (pGES) obtains networks of equal or better quality than GES in less computational time. This improvement is especially noticeable in high-dimensional BNs.

Aesthetic assessment evaluates the quality of a given image using subjective annotations, commonly user ratings, as a knowledge base. Rating complexity is usually relaxed in state-of-the-art works by employing a binary high/low quality label computed from the mean value of rating votes. Nevertheless, this approach introduces uncertainty to average-quality images, which may affect the performance of machine learning models trained from annotated data. In this work, we present a novel approach to aesthetic assessment based on redefining the rating-based groundtruths present in most datasets. Our intent is twofold: to reduce the rating uncertainty and to automatically group them into clusters reflecting high and low quality patterns, thus avoiding an arbitrary threshold like 5 in 1–10 ratings. The experimentation uses the well-known AVA dataset, which consists of more than 255,000 images, and we train several CNN models to test our new groundtruths against the baseline ones. The results show that our approach achieves significant performance gains, between 3% and 9% more balanced accuracy than the baseline groundtruths.

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.

Abstract The multilabel paradigm has recently attracted the attention of the machine learning community, multilabel problems being those which do not have only one class but several binomial classes instead. Although intensive research has been carried on lately into the multilabel classification paradigm, this is not the case of feature subset selection methods. In this work, we propose an adaptation of the well‐known CMIM feature selection algorithm, which is capable of approximating the conditional multivariate mutual information of each candidate attribute with respect to the whole set of labels. This capacity to search any degree of interaction among labels is the reason why our proposal performs better than other state‐of‐the‐art algorithms when the dataset on which it is run contains correlated labels.

Aesthetic classification of images is an inherently subjective task. There does not exist a validated collection of images/photographs labeled as having good or bad quality from experts. Nowadays, the closest approximation to that is to use databases of photos where a group of users rate each image. Hence, there is not a unique good/bad label but a rating distribution given by users voting. Due to this peculiarity, it is not possible to state the problem of binary aesthetic supervised classification in such a direct mode as other Computer Vision tasks. Recent literature follows an approach where researchers utilize the average rates from the users for each image, and they establish an arbitrary threshold to determine their class or label. In this way, images above the threshold are considered of good quality, while images below the threshold are seen as bad quality. This paper analyzes current literature, and it reviews those attributes able to represent an image, differentiating into three families: specific, general and deep features. Among those which have been proved more competitive, we have selected a representative subset, being our main goal to establish a clear experimental framework. Finally, once features were selected, we have used them for the full AVA dataset. We have to remark that to perform validation we report not only accuracy values, which is not that informative in this case, but also, metrics able to evaluate classification power within imbalanced datasets. We have conducted a series of experiments so that distinct well-known classifiers are learned from data. Like that, this paper provides what we could consider valuable and valid baseline results for the given problem.

High Efficiency Video Coding (HEVC) was developed by the Joint Collaborative Team on Video Coding to replace the current H.264/Advanced Video Coding (AVC) standard, which has dominated digital video services in all segments of the domestic and professional markets for over ten years. Therefore, there is a lot of legacy content encoded with H.264/AVC, and an efficient video transcoding from H.264/AVC to HEVC will be needed to enable gradual migration to HEVC. In terms of rate-distortion (RD) performance, HEVC roughly doubles the RD compression performance of H.264/AVC at the expense of a high computational cost. HEVC adopts a quadtree-based coding unit (CU) block partitioning structure that is flexible in adapting various texture characteristics of images. However, this causes a dramatic increase in computational complexity due to the necessity of finding the best CU partitions. This paper presents an adaptive fast quadtree level decision algorithm that is designed to exploit the information gathered at the H.264/AVC decoder in order to make faster decisions on CU splitting in HEVC using a Naïve-Bayes probabilistic classifier that is determined by a supervised data mining process. The experimental results show that the proposed algorithm can achieve a good tradeoff between coding efficiency and complexity compared with the anchor transcoder; moreover, it outperforms other related works available in the literature.

High Efficiency Video Coding was developed by the JCT-VC to replace the current H.264/AVC standard, which has dominated digital video services in all segments of the domestic and professional markets for over ten years. Therefore, there is a lot of legacy content encoded with H.264/AVC, and an efficient video transcoding from H.264 to HEVC will be needed to enable gradual migration to HEVC. HEVC adopts a quad tree-based Coding Unit block partitioning structure that is flexible in adapting various texture characteristics at the expense of a high computational cost. This paper presents a data-driven probabilistic CTU splitting algorithm that is designed to exploit the information gathered at the H.264/AVC decoder in order to make faster decisions on CU splitting in HEVC. Experimental results show that the proposed algorithm can achieve a good tradeoff between coding efficiency and complexity compared with the anchor transcoder, and, moreover, it outperforms other related works available in the literature.

Structural learning of Bayesian networks is a very expensive task even when sacrifying the optimality of the result. Because of that, there are some proposals aimed at obtaining relative-quality solutions in short times. One of them, namely Chain-ACO, searches an ordering among all variables with Ant Colony Optimization and a chain-structured surrogate model, and then uses this ordering to build a Bayesian network by means of the well-known K2 algorithm.

Learning Bayesian networks is known to be an NP-hard problem, and this, combined with the growing interest in learning models from high-dimensional domains, leads to the necessity of finding more efficient learning algorithms. Recent papers have proposed constrained approaches of successfully and widely used local search algorithms, such as Hill Climbing. One of these algorithms families, called constrained Hill Climbing (CHC), greatly improves upon the efficiency of the original approach, obtaining models with slightly lower quality but maintaining their theoretical properties. In this paper, we propose three different modifications to the most scalable version of these algorithms, fast constrained Hill Climbing, to improve the quality of its output by relaxing the constraints imposed to include some diversification in the search process. The aim of these new approaches is to adjust the trade-off between efficiency and accuracy of the algorithm, as they do not modify its complexity and only imply a few more search iterations. We perform an intensive experimental evaluation of the modifications proposed with an extensive comparison between the original algorithms and the new modifications covering several scenarios with quite large data sets. Available code and data for further use of the algorithms presented in this paper and experiment replication can be available at http://simd.albacete.org/supplements/FastCHC.html.

The High Efficiency Video Coding (HEVC) was developed by the Joint Collaborative Team on Video Coding (JCT-VC) to replace the current H.264/AVC standard which has been widely adopted in the last years. Therefore, there is a lot of legacy content encoded with H.264/AVC and an efficient conversion to HEVC is needed. This paper, presents a Fast Quadtree Level Decision (FQLD) algorithm that greatly reduces the complexity of the transcoding process between H.264/AVC and HEVC. The proposal tries to exploit the information gathered at the H.264/AVC decoder to make decisions on Coding Units (CU) splitting in HEVC using a Naïve-Bayes (NB) probabilistic classifier. Experimental results show that the proposed transcoder can achieve a good tradeoff between coding efficiency and complexity.

There exist a wide number of works in the literature related to new systems devoted to manage thermal control in buildings. Commonly, their evaluation is performed by using simulation of users and environmental conditions. Thus, in this work we choose a successful thermal-comfort system, formerly evaluated with simulations, and evaluate it by using data from project ASHRAE RP-884, which provides logs of real data coming from different buildings, in a wide variety of climates, and occupied by people with different thermal preferences. From these logs, we propose a pre-processing and evaluation methodology in order to achieve more realistic evaluations.

There are methods that allow building a Bayesian network when an ordering among variables is provided. Based on them, structural learning of Bayesian networks can be carried out by searching for the ordering which generates the best network, instead of directly searching in the space of Directed Acyclic Graphs. In a previous work, a simple Hill-Climbing algorithm defined over the space of orderings was proposed by the authors. Although it achieves competitive results when comparing with the state of the art algorithms, such as GES, it is not very efficient when the number of variables is high. In this work, we propose a more efficient version of the method that improves its scalability in high dimensional domains and is equivalent to the original. We also propose an asymptotically equivalent algorithm based not only on the orderings, but also on the properties of the underlying network. Besides, we prove the correctness of the operations used in both versions, as well as the correctness of the improvements proposed. The algorithms have been tested over a set of different domains, showing that changes introduced lead to significant reductions on execution time, which become more important as the number of variables grows.

Feature subset selection has become an expensive process due to the relatively recent appearance of high-dimensional databases. Thus, not only the need has arisen for reducing the dimensionality of these datasets, but also for doing it in an efficient way. We propose a new backward search, where attributes are removed given several smart criteria found in the literature and, besides, it is guided using a heuristic which reduces the cost and needed number of evaluations commonly expected from a backward search. Besides, we do not only propose the design of a new forward-backward algorithm but we also provide an experimental study of different criteria to decide the removal of attributes. The result is a very competitive algorithm which does not exceed the in-practice linear complexity while obtaining selected subsets of features with lower cardinality than other state-of-the-art algorithms.

This paper deals with the problem of feature subset selection in classification-oriented datasets with a (very) large number of attributes. In such datasets complex classical wrapper approaches become intractable due to the high number of wrapper evaluations to be carried out. One way to alleviate this problem is to use the so-called filter-wrapper approach or Incremental Wrapper-based Subset Selection (IWSS), which consists of the construction of a ranking among the predictive attributes by using a filter measure, and then a wrapper approach is used by following the rank. In this way the number of wrapper evaluations is linear on the number of predictive attributes. In this paper we present two contributions to the IWSS approach. The first one is related with obtaining more compact subsets, and enables not only the addition of new attributes but also their interchange with some of those already included in the selected subset. Our second contribution, termed early stopping, sets an adaptive threshold on the number of attributes in the ranking to be considered. The advantages of these new approaches are analyzed both theoretically and experimentally. The results over a set of 12 high-dimensional datasets corroborate the success of our proposals.

The COR methodology allows the learning of Linguistic Fuzzy Rule-Based Systems by considering cooperation among rules. In order to do this, it uses search techniques, such as Genetic Algorithms, to find the set of candidate rules which will be used to build the final rule base. The performance of COR algorithms, in terms of the quality of the solutions and cost of the search, decreases as the problem size grows. In this paper, several local search algorithms for learning the rule base are tested, as an alternative to population-based methods. Experiments show that, in most cases, the results for the error of prediction improve upon those obtained with Genetic Algorithms. Moreover, this proposal allows a drastic reduction in the computational effort required to find the solutions.

This work studies the problem of premature convergence due to the lack of diversity in Estimation of Distributions Algorithms. This problem is quite important for these kind of algorithms since, even when using very complex probabilistic models, they can not solve certain optimization problems such as some deceptive, hierarchical or multimodal ones.

This paper deals with the problem of wrapper-based feature subset selection in classification oriented datasets with a (very) large number of attributes. In such datasets sophisticated search algorithms like beam search, branch and bound, best first, genetic algorithms, etc., become intractable in the wrapper approach due to the high number of wrapper evaluations to be carried out. One way to alleviate this problem is to use the so-called filter-wrapper approach or Incremental Wrapper-based Subset Selection (IWSS), which consists in the construction of a ranking among the predictive attributes by using a filter measure, and then a wrapper approach is used guided by the rank. In this way the number of wrapper evaluations is linear with the number of predictive attributes. In this paper we present a contribution to the IWSS approach which helps it to obtain more compact subsets, and consists into allow not only the addition of new attributes but also the interchange with some of the already included in the selected subset. The disadvantage of this novelty is that it grows up the worst-case complexity of IWSS up to O(n2), however, as in the case of the well known sequential forward selection (SFS) the actual number of wrapper evaluations is considerably smaller. Empirical tests over 7 (biological) datasets with a large number of attributes demonstrate the success of the proposed approach when comparing with both IWSS and SFS.

AODE (Aggregating One-Dependence Estimators) is considered one of the most interesting representatives of the Bayesian classifiers, taking into account not only the low error rate it provides but also its efficiency. Until now, all the attributes in a dataset have had to be nominal to build an AODE classifier or they have had to be previously discretized. In this paper, we propose two different approaches in order to deal directly with numeric attributes. One of them uses conditional Gaussian networks to model a dataset exclusively with numeric attributes; and the other one keeps the superparent on each model discrete and uses univariate Gaussians to estimate the probabilities for the numeric attributes and multinomial distributions for the categorical ones, it also being able to model hybrid datasets. Both of them obtain competitive results compared to AODE, the latter in particular being a very attractive alternative to AODE in numeric datasets.

Structural learning of Bayesian networks (BNs) is an NP-hard problem generally addressed by means of heuristic search algorithms. Although these techniques do not guarantee an optimal result, they allow obtaining good solutions with a relatively low computational effort. Many proposals are based on searching the space of directed acyclic graphs. However, there are alternatives consisting of exploring the space of equivalence classes of BNs, which yields more complex and difficult to implement algorithms, or the space of the orderings among variables. In practice, ordering-based methods allow reaching good results, but, they are costly in terms of computation. In this paper, we prove the correctness of the method used to evaluate each permutation when exploring the space of orderings, and we propose two simple and efficient learning algorithms based on this approach. The first one is a Hill climbing method which uses an improved neighbourhood definition, whereas the second algorithm is its natural extension based on the well-known variable neighbourhood search metaheuristic. The algorithms have been tested over a set of different domains in order to study their behaviour in practice.

One of the key points in Estimation of Distribution Algorithms (EDAs) is the learning of the probabilistic graphical model used to guide the search: the richer the model the more complex the learning task. Dependency networks-based EDAs have been recently introduced. On the contrary of Bayesian networks, dependency networks allow the presence of directed cycles in their structure. In a previous work the authors proposed EDNA, an EDA algorithm in which a multivariate dependency network is used but approximating its structure learning by considering only bivariate statistics. EDNA was compared with other models from the literature with the same computational complexity (e.g., univariate and bivariate models). In this work we propose a modified version of EDNA in which not only the structural learning phase is limited to bivariate statistics, but also the simulation and the parameter learning task. Now, we extend the comparison employing multivariate models based on Bayesian networks (EBNA and hBOA). Our experiments show that the modified EDNA is more accurate than the original one, being its accuracy comparable to EBNA and hBOA, but with the advantage of being faster specially in the more complex cases.

In this paper we deal with the problem of automatically optimizing the gait of a robot for forward walking speed. Each different walking surface and/or the wear and tear of the robots determines the speed of the robot. This means that a specific gait for one surface may not be valid on another surface or even on the same surface some time later. Given a parametrized walk designed for the robot and one specific robot, we approach the problem of searching over the space of gaits for this robot by using an estimation of distribution algorithm and our knowledge of the problem, which allows us to considerably reduce the space of gaits over which the algorithm searches. We have implemented and tested our method using the Sony AIBO ERS-7 robot, significantly improving on our previous gait in a short period of training time.

The main feature of Estimation of Distribution Algorithms is the way they evolve by gathering the information about the best elements of each population into a probability distribution. This work studies the application of these algorithms to the learning of weighted linguistic fuzzy-rule-based systems with the wCOR method. For this purpose, we propose the use of two different probabilistic models: One which does not assume any dependence between the rule consequents and their weights, and other whose structure is fixed from these dependences.

Migration of probabilistic models instead of individuals has been shown beneficial in islands-based models of parallel univariate estimation of distribution algorithms (EDAs). One of the key points when using this type of migration is how to incorporate the incoming probabilistic model to the inner one in a given island. When dealing with combinatorial optimization problems and univariate EDAs, models can be combined successfully by using a convex combination of the two probabilistic models (delaOssa et al., 2004). In this paper, we present an alternative way of combining probabilistic models. The new proposal for model combination is based on local search methods, and has its motivation in trying to identify what parts of the incoming model can help to improve the inner one, and to use only these parts to update the incoming model, instead of updating the whole one. Several algorithms are proposed and evaluated by using different test problems. The experiments show that the new proposals perform better than those based on convex combination, especially in the most difficult test problems.

A common approach for learning Bayesian networks (BNs) from data is based on the use of a scoring metric to evaluate the fitness of any given candidate network to the data and a method to explore the search space, which usually is the set of directed acyclic graphs (DAGs). The most efficient search methods used in this context are greedy hill climbing, either deterministic or stochastic. One of these methods that has been applied with some success is hill climbing with random restart. In this article we study a new algorithm of this type to restart a local search when it is trapped at a local optimum. It uses problem-specific knowledge about BNs and the information provided by the database itself (by testing the conditional independencies, which are true in the current solution of the search process). We also study a new definition of neighborhood for the space of DAGs by using the classical operators of arc addition and arc deletion together with a new operator for arc reversal. The proposed methods are empirically tested using two different domains: ALARM and INSURANCE. © 2003 Wiley Periodicals, Inc.