Nahla Ben Amor

Decision trees as possibilistic classifiers

This paper addresses the classification problem with imperfect data. More precisely, it extends standard decision trees to handle uncertainty in both building and classification procedures. Uncertainty here is represented by means of possibility distributions. The first part investigates the issue of building decision trees from data with uncertain class values by developing a non-specificity based gain ratio as the attribute selection measure which, in our case, is more appropriate than the standard gain ratio based on Shannon entropy. The proposed non-specificity based possibilistic decision tree (NS-PDT) approach is then extended by considering another kind of uncertainty inherent in the building procedure. The extended approach so-called non-specificity based possibilistic option decision tree (NS-PODT) offers a more flexible building procedure by allowing the selection of more than one attribute in each node. The second part addresses the classification phase. More specifically, it investigates the issue of predicting the class value of new instances presented with certain and/or uncertain attribute values. Finally, we have developed a possibilistic decision tree toolbox (PD2T) in order to show the feasibility of the proposed approach.

Naïve possibilistic network classifiers

Naive Bayesian network classifiers have proved their effectiveness to accomplish the classification task, even if they work under the strong assumption of independence of attributes in the context of the class node. However, as all of them are based on probability theory, they run into problems when they are faced with imperfection. This paper proposes a new approach of classification under the possibilistic framework with naive classifiers. To output the naive possibilistic network classifier, two procedures are studied namely the building phase, which deals with imperfect (imprecise/uncertain) dataset attributes and classes, and the classification phase, which is used to classify new instances that may be characterized by imperfect attributes. To improve the performance of our classifier, we propose two extensions namely selective naive possibilistic classifier and semi-naive possibilistic classifier. Experimental study has shown naive Bayes style possibilistic classifier, and is efficient in the imperfect case.

Information Affinity: A New Similarity Measure for Possibilistic Uncertain Information

This paper addresses the issue of measuring similarity between pieces of uncertain information in the framework of possibility theory. In a first part, natural properties of such functions are proposed and a survey of the few existing measures is presented. Then, a new measure so-called Information Affinity is proposed to overcome the limits of the existing ones. The proposed function is based on two measures, namely, a classical informative distance, e.g. Manhattan distance which evaluates the difference, degree by degree, between two normalized possibility distributions and the well known inconsistency measure which assesses the conflict between the two possibility distributions. Some potential applications of the proposed measure are also mentioned in this paper.

Qualitative possibilistic influence diagrams based on qualitative possibilistic utilities

This paper proposes a new approach for decision making under uncertainty based on influence diagrams and possibility theory. The so-called qualitative possibilistic influence diagrams extend standard influence diagrams in order to avoid difficulties attached to the specification of both probability distributions relative to chance nodes and utilities relative to value nodes. In fact, generally, it is easier for experts to quantify dependencies between chance nodes qualitatively via possibility distributions and to provide a preferential relation between different consequences. In such a case, the possibility theory offers a suitable modeling framework. Different combinations of the quantification between chance and utility nodes offer several kinds of possibilistic influence diagrams. This paper focuses on qualitative ones and proposes an indirect evaluation method based on their transformation into possibilistic networks. The proposed approach is implemented via a possibilistic influence diagram toolbox (PIDT).

Graphoid properties of qualitative possibilistic independence relations

Independence relations play an important role in uncertain reasoning based on Bayesian networks. In particular, they are useful in decomposing joint distributions into more elementary local ones. Recently, in a possibility theory framework, several qualitative independence relations have been proposed, where uncertainty is encoded by means of a complete pre-order between states of the world. This paper studies the well-known graphoid properties of these qualitative independences. Contrary to the probabilistic independence, several qualitative independence relations are not necessarily symmetric. Therefore, we also analyze the symmetric counterparts of graphoid properties (called reverse graphoid properties).

Brain Tumor Segmentation Using Support Vector Machines

One of the challenging tasks in the medical area is brain tumor segmentation which consists on the extraction process of tumor regions from images. Generally, this task is done manually by medical experts which is not always obvious due to the similarity between tumor and normal tissues and the high diversity in tumors appearance. Thus, automating medical image segmentation remains a real challenge which has attracted the attention of several researchers in last years. In this paper, we will focus on segmentation of Magnetic Resonance brain Images (MRI). Our idea is to consider this problem as a classification problem where the aim is to distinguish between normal and abnormal pixels on the basis of several features, namely intensities and texture. More precisely, we propose to use Support Vector Machine (SVM) which is within popular and well motivating classification methods. The experimental study will be carried on Gliomas dataset representing different tumor shapes, locations, sizes and image intensities.

SemCaDo: a serendipitous strategy for learning causal Bayesian networks using ontologies

Learning Causal Bayesian Networks (CBNs) is a new line of research in the machine learning field. Within the existing works in this direction [8,12,13], few of them have taken into account the gain that can be expected when integrating additional knowledge during the learning process. In this paper, we present a new serendipitous strategy for learning CBNs using prior knowledge extracted from ontologies. The integration of such domains semantic information can be very useful to reveal new causal relations and provide the necessary knowledge to anticipate the optimal choice of experimentations. Our strategy also supports the evolving character of the semantic background by reusing the causal discoveries in order to enrich the domain ontologies.

Learning Causal Bayesian Networks from Incomplete Observational Data and Interventions

This paper proposes a new method for learning causal Bayesian networks from incomplete observational data and interventions. We extend our Greedy Equivalence Search-Expectation Maximization (GES-EM) algorithm [2], initially proposed to learn Bayesian networks from incomplete observational data, by adding a new step allowing the discovery of correct causal relationships using interventional data. Two intervention selection approaches are proposed: an adaptive one, where interventions are done sequentially and where the impact of each intervention is considered before starting the next one, and a non-adaptive one, where the interventions are executed simultaneously. An experimental study shows the merits of the new version of the GES-EM algorithm by comparing the two selection approaches.

Optimization algorithms for multi-objective problems with fuzzy data

This paper addresses multi-objective problems with fuzzy data which are expressed by means of triangular fuzzy numbers. In our previous work, we have proposed a fuzzy Pareto approach for ranking the generated triangular-valued functions. Then, since the classical multi-objective optimization methods can only use crisp values, we have applied a defuzzification process. In this paper, we propose a fuzzy extension of two well-known multi-objective evolutionary algorithms: SPEA2 and NSGAII by integrating the fuzzy Pareto approach and by adapting their classical techniques of diversity preservation to the triangular fuzzy context. An application on multi-objective Vehicle Routing Problem (VRP) with uncertain demands is finally proposed and evaluated using some experimental tests.

Possibilistic sequential decision making

When the information about uncertainty cannot be quantified in a simple, probabilistic way, the topic of possibilistic decision theory is often a natural one to consider. The development of possibilistic decision theory has lead to the proposition a series of possibilistic criteria, namely: optimistic and pessimistic possibilistic qualitative criteria [7], possibilistic likely dominance [2] and [9], binary possibilistic utility [11] and possibilistic Choquet integrals [24]. This paper focuses on sequential decision making in possibilistic decision trees. It proposes a theoretical study on the complexity of the problem of finding an optimal strategy depending on the monotonicity property of the optimization criteria – when the criterion is transitive, this property indeed allows a polytime solving of the problem by Dynamic Programming. We show that most possibilistic decision criteria, but possibilistic Choquet integrals, satisfy monotonicity and that the corresponding optimization problems can be solved in polynomial time by Dynamic Programming. Concerning the possibilistic likely dominance criteria which is quasi-transitive but not fully transitive, we propose an extended version of Dynamic Programming which remains polynomial in the size of the decision tree. We also show that for the particular case of possibilistic Choquet integrals, the problem of finding an optimal strategy is NP-hard. It can be solved by a Branch and Bound algorithm. Experiments show that even not necessarily optimal, the strategies built by Dynamic Programming are generally very good.