Carlos J. Mantas’s research while affiliated with University of Granada and other places

Multi-Label Classification (MLC) assumes that each instance belongs to a set of labels, unlike traditional classification, where each instance corresponds to a unique value of a class variable. Calibrated Label Ranking (CLR) is an MLC algorithm that determines a ranking of labels for a given instance by considering a binary classifier for each pair of labels. In this way, it exploits pairwise label correlations. Furthermore, CLR alleviates the class imbalance problem that usually arises in MLC because, in this domain, very few instances often belong to a label. In order to build the binary classifiers in CLR, it is required to employ a standard classification algorithm. The Decision Tree method C4.5 has been widely used in this field. In this research, we show that a version of C4.5 based on imprecise probabilities recently proposed, known as Credal C4.5, is more appropriate than C4.5 to handle the binary classification tasks in CLR. Experimental results reveal that Credal C4.5 outperforms C4.5 when both methods are used in CLR and that the difference is more statistically significant as the label noise level is higher.

In Multi-Label Classification (MLC), Classifier Chains (CC) are considered simple and effective methods to exploit correlations between labels. A CC considers a binary classifier per label, in which the previous labels, according to an established order, are used as additional features. The label order strongly influences the performance of the CC, and there is no way to determine the optimal order so far. In this work, a new label ordering method based on label correlations is proposed. It uses a non-parametric model based on imprecise probabilities to estimate the correlations between pairs of labels. Then, it employs a greedy procedure that, to insert the labels in the chain, considers the correlations among the candidate labels and the ones already inserted, as well as the correlations between the candidate labels and the ones non-inserted yet. We argue that our proposal presents some advantages over the label ordering methods in CC developed so far based on label correlations. It is also shown that our proposal achieves better experimental results than the label ordering methods proposed so far that use label correlations in CC.

The Naive Credal Classifier (NCC) was the first method proposed for Imprecise Classification. It starts from the known Naive Bayes algorithm (NB), which assumes that the attributes are independent given the class variable. Despite this unrealistic assumption, NB and NCC have been successfully used in practical applications. In this work, we propose a new version of NCC, called Extreme Prior Naive Credal Classifier (EP-NCC). Unlike NCC, EP-NCC takes into consideration the lower and upper prior probabilities of the class variable in the estimation of the lower and upper conditional probabilities. We demonstrate that, with our proposed EP-NCC, the predictions are more informative than with NCC without increasing the risk of making erroneous predictions. An experimental analysis carried out in this work shows that EP-NCC significantly outperforms NCC and obtains statistically equivalent results to the algorithm proposed so far for Imprecise Classification based on decision trees, even though EP-NCC is computationally simpler. Therefore, EP-NCC is more suitable to be applied to large datasets for Imprecise Classification than the methods proposed so far in this field. This is an important issue in favor of our proposal due to the increasing amount of data in every area.

A Bayesian Network (BN) is a graphical structure, with associated conditional probability tables. This structure allows us to obtain different knowledge than the one obtained from standard classifiers. With a BN, representing a dataset, we can calculate different probabilities about a set of features with respect to other ones. This inference can be more powerful than the one obtained from classifiers. A BN can be built from data and have analytical and diagnostic capabilities that make it very suitable for credit domains. Credit scoring and risk analysis are fundamental tasks for financial institutions with the aim to avoid important losses. In these tasks and other domains, an excessive number of features can convert a BN into a complex and difficult to interpret model, but a few number of features can represent a loss of information obtained from data. A new method based on imprecise probabilities is presented to select an informative subset of features. Using this new feature selection method, we can build a BN that has an excellent adjustment to the data, considering a reduced number of features. Via a set of experiments, it is shown that the adjustment is better than the ones obtained with no previous variable selection method and with a similar and successful variable subset selection method based on precise probabilities. Finally, a BN is built with two important characteristics: (i) it represents a better adjustment to the data; and (ii) it has a low complexity (better interpretability) due to the small number of important selected features. A practical example about inference on a BN to help on credit risk analysis is also presented.

Within the field of supervised classification, the naïve Bayes (NB) classifier is a very simple and fast classification method that obtains good results, being even comparable with much more complex models. It has been proved that the NB model is strongly dependent on the estimation of conditional probabilities. In the literature, it had been shown that the classical and Laplace estimations of probabilities have some drawbacks and it was proposed a NB model that takes into account the a priori probabilities in order to estimate the conditional probabilities, which was called m-probability-estimation. With a very scarce experimentation, this approximation based on m-probability-estimation demonstrated to provide better results than NB with classical and Laplace estimations of probabilities. In this research, a new naïve Bayes variation is proposed, which is based on the m-probability-estimation version and takes into account imprecise probabilities in order to calculate the a priori probabilities. An exhaustive experimental research is carried out, with a large number of data sets and different levels of class noise. From this experimentation, we can conclude that the proposed NB model and the m-probability-estimation approach provide better results than NB with classical and Laplace estimation of probabilities. It will be also shown that the proposed NB implies an improvement over the m-probability-estimation model, especially when there is some class noise.

In many situations, classifiers predict a set of states of a class variable because there is no information enough to point only one state. In the data mining area, this task is known as Imprecise Classification. Decision Trees that use imprecise probabilities, also known as Credal Decision Trees (CDTs), have been adapted to this field. The adaptation proposed so far uses the Imprecise Dirichlet Model (IDM), a mathematical model of imprecise probabilities that assumes prior knowledge about the data, depending strongly on a hyperparameter. This strong dependence is solved with the Non-Parametric Predictive Inference Model (NPI-M), also based on imprecise probabilities. This model does not make any prior assumption of the data and does not have parameters. In this work, we propose a new adaptation of CDTs to Imprecise Classification based on the NPI-M. An experimental study carried out in this research shows that the adaptation with NPI-M has an equivalent performance than the one obtained with the adaptation based on the IDM with the best choice of the hyperparameter. Consequently, since the NPI-M is a non-parametric approach, it is concluded that the NPI-M is more appropriated than the IDM to be applied to the adaptation of CDTs to Imprecise Classification.

Decision Trees (DTs) have been adapted to Multi-Label Classification (MLC). These adaptations are known as Multi-Label Decision Trees (ML-DT). In this research, a new ML-DT based on the Nonparametric Predictive Inference Model on Multinomial data (NPI-M) is proposed. The NPI-M is an imprecise probabilities model that provides good results when it is applied to DTs in standard classification. Unlike other models based on imprecise probabilities, the NPI-M is a nonparametric approach and it does not make unjustified assumptions before observing data. It is shown that the new ML-DT based on the NPI-M is more robust to noise than the ML-DT based on precise probabilities. As the intrinsic noise in MLC might be higher than in traditional classification, it is expected that the new ML-DT based on the NPI-M outperforms the already existing ML-DT. This fact is validated with an exhaustive experimentation carried out in this work on different MLC datasets with several levels of added noise. In it, many MLC evaluation metrics are employed in order to measure the performance of the algorithms. The experimental analysis shows that the proposed ML-DT based on NPI-M obtains better results than the ML-DT that uses precise probabilities, especially when we work on data with noise.

Random forest (RF) is an ensemble learning method, and it is considered a reference due to its excellent performance. Several improvements in RF have been published. A kind of improvement for the RF algorithm is based on the use of multivariate decision trees with local optimization process (oblique RF). Another type of improvement is to provide additional diversity for the univariate decision trees by means of the use of imprecise probabilities (random credal random forest, RCRF). The aim of this work is to compare experimentally these improvements of the RF algorithm. It is shown that the improvement in RF with the use of additional diversity and imprecise probabilities achieves better results than the use of RF with multivariate decision trees.

The Credal Decision Trees (CDT) have been adapted for Imprecise Classification (ICDT). However, no ensembles of imprecise classifiers have been proposed so far. The reason might be that it is not a trivial question to combine the predictions made by multiple imprecise classifier. In fact, if the combination method used is not appropriate, the ensemble method could even worse the performance of one single classifier. On the other hand, the Bagging scheme has shown to provide satisfactory results in precise classification, specially when it is used with CDTs, which are known to be very weak and unstable classifiers. For these reasons, in this research, it is proposed a new Bagging scheme with ICDTs. It is presented a new technique for combining predictions made by imprecise classifiers that tries to maximize the precision of the bagging classifier. If the procedure for such a combination is too conservative it is easy to obtain few information and worse the results of a single classifier. Our proposal considers only the states with the minimum level of non-dominance. An exhaustive experimentation carried out in this work has shown that the Bagging of ICDTs, with our proposed combination technique, performs clearly better than a single ICDT.