Joaquín Abellán

Building classification trees using the total uncertainty criterion

We present an application of the measure of total uncertainty on convex sets of probability distributions, also called credal sets, to the construction of classification trees. In these classification trees the probabilities of the classes in each one of its leaves is estimated by using the imprecise Dirichlet model. In this way, smaller samples give rise to wider probability intervals. Branching a classification tree can decrease the entropy associated with the classes but, at the same time, as the sample is divided among the branches the nonspecificity increases. We use a total uncertainty measure (entropy + nonspecificity) as branching criterion. The stopping rule is not to increase the total uncertainty. The good behavior of this procedure for the standard classification problems is shown. It is important to remark that it does not experience of overfitting, with similar results in the training and test samples.

Improving experimental studies about ensembles of classifiers for bankruptcy prediction and credit scoring

Previous studies about ensembles of classifiers for bankruptcy prediction and credit scoring have been presented. In these studies, different ensemble schemes for complex classifiers were applied, and the best results were obtained using the Random Subspace method. The Bagging scheme was one of the ensemble methods used in the comparison. However, it was not correctly used. It is very important to use this ensemble scheme on weak and unstable classifiers for producing diversity in the combination. In order to improve the comparison, Bagging scheme on several decision trees models is applied to bankruptcy prediction and credit scoring. Decision trees encourage diversity for the combination of classifiers. Finally, an experimental study shows that Bagging scheme on decision trees present the best results for bankruptcy prediction and credit scoring.

Upper entropy of credal sets. Applications to credal classification

We present an application of the measure of entropy for credal sets: as a branching criterion for constructing classification trees based on imprecise probabilities which are determined with the imprecise Dirichlet model. We also justify the use of upper entropy as a global uncertainty measure for credal sets and present a deduction of this measure. We have carried out several experiments in which credal classification trees are built taking a global uncertainty measure as a basis. The results show how the introduced methodology improves the performance of traditional methods (Naive Bayes and C4.5), by providing a much lower error rate.

Maximum of entropy for credal sets

In belief functions, there is a total measure of uncertainty that quantify the lack of knowledge and verifies a set of important properties. It is based on two measures: maximum of entropy and non-specificity. In this paper, we prove that the maximum of entropy verifies the same set of properties in a more general theory as credal sets and we present an algorithm that finds the probability distribution of maximum entropy for another interesting type of credal sets as probability intervals.

Analysis of traffic accident severity using Decision Rules via Decision Trees

A Decision Tree (DT) is a potential method for studying traffic accident severity. One of its main advantages is that Decision Rules (DRs) can be extracted from its structure. And these DRs can be used to identify safety problems and establish certain measures of performance. However, when only one DT is used, rule extraction is limited to the structure of that DT and some important relationships between variables cannot be extracted. This paper presents a more effective method for extracting rules from DTs. The methods effectiveness when applied to a particular traffic accident dataset is shown. Specifically, our study focuses on traffic accident data from rural roads in Granada (Spain) from 2003 to 2009 (both included). The results show that we can obtain more than 70 relevant rules from our data using the new method, whereas with only one DT we would have extracted only five relevant rules from the same dataset.

Disaggregated total uncertainty measure for credal sets

We present a new approach to measure uncertainty/information applicable to theories based on convex sets of probability distributions, also called credal sets. A definition of a total disaggregated uncertainty measure on credal sets is proposed in this paper motivated by recent outcomes. This definition is based on the upper and lower values of Shannons entropy for a credal set. We justify the use of the proposed total uncertainty measure and the parts into which it is divided: the maximum difference of entropies, which can be used as a non-specificity measure (imprecision), and the minimum of entropy, which represents a measure of conflict (contradiction).

Requirements for total uncertainty measures in Dempster–Shafer theory of evidence

Recently, an alternative measure of total uncertainty in Dempster–Shafer theory of evidence (DST) has been proposed in place of the maximum entropy measure. It is based on the pignistic probability of a basic probability assignment and it is proved that this measure verifies a set of needed properties for such a type of measure. The proposed measure is motivated by the problems that maximum (upper) entropy has. In this paper, we analyse the requirements, presented in the literature, for total uncertainty measures in DST and the shortcomings found on them. We extend the set of requirements, which we consider as a set of requirements of properties, and we use the set of shortcomings found on them to define a set of requirements of the behaviour for total uncertainty measures in DST. We present the differences of the principal total uncertainty measures presented in DST taking into account their properties and behaviour. Also, an experimental comparative study of the performance of total uncertainty measures in DST on a special type of belief decision trees is presented.

Uncertainty measures on probability intervals from the imprecise Dirichlet model

When we use a mathematical model to represent information, we can obtain a closed and convex set of probability distributions, also called a credal set. This type of representation involves two types of uncertainty called conflict (or randomness) and non-specificity, respectively. The imprecise Dirichlet model (IDM) allows us to carry out inference about the probability distribution of a categorical variable obtaining a set of a special type of credal set (probability intervals). In this paper, we shall present tools for obtaining the uncertainty functions on probability intervals obtained with the IDM, which can enable these functions in any application of this model to be calculated.

An ensemble method using credal decision trees

Supervised classification learning can be considered as an important tool for decision support. In this paper, we present a method for supervised classification learning, which ensembles decision trees obtained via convex sets of probability distributions (also called credal sets) and uncertainty measures. Our method forces the use of different decision trees and it has mainly the following characteristics: it obtains a good percentage of correct classifications and an improvement in time of processing compared with known classification methods; it not needs to fix the number of decision trees to be used; and it can be parallelized to apply it on very large data sets.

A non-specificity measure for convex sets of probability distributions

In belief functions, there are two types of uncertainty which are due to lack of knowledge: randomness and non-specificity. In this paper, we present a non-specificity measure for convex sets of probability distributions that generalizes Dubois and Prades non-specificity measure in the Dempster-Shafer theory of evidence.