Naive possibilistic classifiers for imprecise or uncertain numerical data

Abstract

In real-world problems, input data may be pervaded with uncertainty. In this paper, we investigate the behavior of naive possibilistic classifiers, as a counterpart to naive Bayesian ones, for dealing with classification tasks in presence of uncertainty. For this purpose, we extend possibilistic classifiers, which have been recently adapted to numerical data, in order to cope with uncertainty in data representation. Here the possibility distributions that are used are supposed to encode the family of Gaussian probabilistic distributions that are compatible with the considered data set. We consider two types of uncertainty: i) the uncertainty associated with the class in the training set, which is modeled by a possibility distribution over class labels, and ii) the imprecision pervading attribute values in the testing set represented under the form of intervals for continuous data. Moreover, the approach takes into account the uncertainty about the estimation of the Gaussian distribution parameters due to the limited amount of data available. We first adapt the possibilistic classification model, previously proposed for the certain case, in order to accommodate the uncertainty about class labels. Then, we propose an algorithm based on the extension principle to deal with imprecise attribute values. The experiments reported show the interest of possibilistic classifiers for handling uncertainty in data. In particular, the probability-to-possibility transform-based classifier shows a robust behavior when dealing with imperfect data.

A New Hybrid Possibilistic-Probabilistic Decision-Making Scheme for Classification

“…This decision-making criterion is called the Naive Bayes style possibilistic criterion Refs. [ 40 , 41 , 42 ] and most ongoing efforts are oriented into the computation of the a posteriori possibility values using numerical data [ 43 ]. An extensive study of properties and equivalence between possibilistic and probability approaches is presented in [ 20 ].…”

A hybrid possibilistic approach for Arabic full morphological disambiguation

“…Ambiguity, imprecision and uncertainty: we treat morphological disambiguation as a classification task with imperfect data. In possibility theory, imperfection covers both imprecise and uncertain data [34,64]. In our case, imperfection is caused by morphological ambiguities.…”

“…The combination of the necessity and possibility measures is inspired from the possibilistic Information Retrieval and Knowledge Extraction Systems [32,[37][38][39][40][62][63][64][65]67]. …”

An evolving possibilistic fuzzy modeling approach for Value-at-Risk estimation

“…The PFCM simultaneously produces memberships and typicalities to alleviate outliers and noisy data sensitivity of traditional fuzzy clustering approaches, yet avoids coincident clusters [42,26]. The advantages of PFCM have been emphasized in the literature [49,19,10]. Using traditional benchmarks of time seriess forecasting problems, [38] showed the high potential of rPFM when dealing with nonlinear and nonstationary systems affected by noise and outliers.…”