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Upper entropy of credal sets. Applications to credal classification

Joaquín Abellán, Serafín Moral
2005 International Journal of Approximate Reasoning  
We also justify the use of upper entropy as a global uncertainty measure for credal sets and present a deduction of this measure.  ...  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  ...  It is simple to compute the upper entropy of this credal set (a general algorithm applicable to probability intervals can be found in [3] ).  ... 
doi:10.1016/j.ijar.2004.10.001 fatcat:o7vwbjq7lzckxnlkk5oqjgrww4

Application of uncertainty measures on credal sets on the naive Bayesian classifier

Joaquín Abellán
2006 International Journal of General Systems  
Acknowledgements This work has been supported by the Spanish Ministry of Science and Technology under the Algra project (TIN2004-06204-C03-02).  ...  In the line of this future work, we shall also consider the use of credal sets and information measures to complete data preprocessing prior to the application of a classification method that can help  ...  Our proposal is to use the IDM model to represent the information by means of a credal set and to obtain the value of the uncertainty by applying the maximum entropy function on the obtained credal set  ... 
doi:10.1080/03081070600867039 fatcat:c4dg5ewk2jgorgo2bvznsk4cwy

Disaggregated total uncertainty measure for credal sets

J. Abellán, G.J. Klir, S. Moral
2006 International Journal of General Systems  
We present a new approach to measure uncertainty/information applicable to theories based on convex sets of probability distributions, also called credal sets.  ...  This definition is based on the upper and lower values of Shannon's entropy for a credal set.  ...  Acknowledgements This work has been supported by the Spanish Ministry of Science and Technology under project Algra (TIN2004-06204-C03-02).  ... 
doi:10.1080/03081070500473490 fatcat:umuvumc6incidixqbikmdn5mzy

Building classification trees using the total uncertainty criterion

Joaquín Abellán, Serafín Moral
2003 International Journal of Intelligent Systems  
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.  ...  We use a total uncertainty measure (entropy ϩ nonspecificity) as branching criterion. The stopping rule is not to increase the total uncertainty.  ...  Acknowledgments We would like to thank Marco Zaffalon for his interesting and insightful comments and suggestions.  ... 
doi:10.1002/int.10143 fatcat:pp6uwvdcqbgijf2wsgetvpnh6m

Uncertainty measures on probability intervals from the imprecise Dirichlet model

J. Abellán
2006 International Journal of General Systems  
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.  ...  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)  ...  We have developed and proved results and algorithms to obtain important uncertainty measures on this type of credal sets: maximum of entropy, minimum of entropy and Hartley measure.  ... 
doi:10.1080/03081070600687643 fatcat:fsrjv4r545a4bg2xs3lad4vcvu

Credal-C4.5: Decision tree based on imprecise probabilities to classify noisy data

Carlos J. Mantas, Joaquín Abellán
2014 Expert systems with applications  
In the area of classification, C4.5 is a known algorithm widely used to design decision trees. In this algorithm, a pruning process is carried out to solve the problem of the over-fitting.  ...  In this manner, Credal-C4.5 builds trees for solving classification problems assuming that the training set is not fully reliable.  ...  We think that it can be very interesting to apply Credal-C4.5 algorithm on data sets of real applications, to analyze results and to extract knowledge about the application from the credal tree.  ... 
doi:10.1016/j.eswa.2014.01.017 fatcat:rio5hkwsnbfdhmoltlu3wrtidq

Maximum of entropy for belief intervals under Evidence Theory

Serafin Moral-Garcia, Joaquin Abellan
2020 IEEE Access  
Moreover, its calculation is notably easier than the upper entropy on the credal set associated with the BPA.  ...  In this research, we develop a new uncertainty measure that consists of the maximum of entropy on the credal set corresponding to belief intervals for singletons.  ...  In consequence, our proposed measure is more suitable to be used in practical applications than the upper entropy on the credal set associated with a BPA.  ... 
doi:10.1109/access.2020.3003715 fatcat:7kyohtdgmfhsxlcr76vihbhcsi

Credible classification for environmental problems

M ZAFFALON
2005 Environmental Modelling & Software  
This paper shows empirically, on an agricultural data set, that established methods of classification do not always adhere to this principle.  ...  With credal classification, conditions of ignorance may limit the power of the inferences, not the credibility of the predictions.  ...  Acknowledgments I would like to thank Peter Walley for enlightening discussions and for encouraging me to develop credal classification.  ... 
doi:10.1016/j.envsoft.2004.10.006 fatcat:rc6uz7j645cbhjb6fzxlirjoze

Reliable Knowledge-Based Adaptive Tests by Credal Networks [chapter]

Francesca Mangili, Claudio Bonesana, Alessandro Antonucci
2017 Lecture Notes in Computer Science  
We suggest the use of credal networks, a generalization of Bayesian networks based on sets of probability mass functions, to implement adaptive tests exploiting the knowledge of the test developer instead  ...  reducing the number of questions required to do it.  ...  Adaptive Testing by Credal Networks Credal sets and credal networks. A set of PMFs over X i is called here credal set (CS) and denoted as K(X i ).  ... 
doi:10.1007/978-3-319-61581-3_26 fatcat:lx4irji4hffv3ggn2fdomdmv4a

Credal Classification based on AODE and compression coefficients [article]

Giorgio Corani, Alessandro Antonucci
2012 arXiv   pre-print
We address this problem by the paradigm of credal classification, namely by substituting the unique prior with a set of priors.  ...  Experiments show that both credal classifiers provide higher classification reliability than their determinate counterparts; moreover the compression-based credal classifier compares favorably to previous  ...  We address this problem by adopting the paradigm of credal classification Corani and Zaffalon, 2008b) , namely drop-ping the unique prior in favor of a set of priors (prior credal set) (Levi, 1980) .  ... 
arXiv:1203.5716v2 fatcat:7chdczhbrvgbpixnnw6ylswcye

Credal ensembles of classifiers

G. Corani, A. Antonucci
2014 Computational Statistics & Data Analysis  
To robustly deal with the choice of the prior, the single prior over the models is substituted by a set of priors over the models (credal set), thus obtaining a credal ensemble of Bayesian classifiers.  ...  When faced with prior-dependent instances, the credal ensemble remains reliable by returning a set of classes rather than a single class.  ...  We discretize numerical features by the entropy-based method of Fayyad and Irani (1993) . For the implementation of all credal sets, we set = 0.01.  ... 
doi:10.1016/j.csda.2012.11.010 fatcat:draf3iylanh2betuaaafe4yqhe

Credibility via imprecise probability

Marco Zaffalon
2005 International Journal of Approximate Reasoning  
In the first, Abellán and Moral investigate the application to pattern classification of a measure of entropy for sets of distributions (also called credal sets).  ...  They do this in the setting of multiple priors, by extending a well known classification tree to credal sets originated by the imprecise Dirichlet model. The results are important and twofold.  ... 
doi:10.1016/j.ijar.2004.11.001 fatcat:nyqfxqxw4bfvbgsogskm22ojue

Classification with decision trees from a nonparametric predictive inference perspective

Joaquín Abellán, Rebecca M. Baker, Frank P.A. Coolen, Richard J. Crossman, Andrés R. Masegosa
2014 Computational Statistics & Data Analysis  
We present an application of Nonparametric Predictive Inference for multinomial data (NPI-M) in classification tasks.  ...  any format or medium without the formal permission of the copyright holders.  ...  The work of Richard Crossman was partly funded by the UK National Institute for Health Research.  ... 
doi:10.1016/j.csda.2013.02.009 fatcat:htgvdecajzfytdhlilwlgnrzxa

Improving the Naive Bayes Classifier via a Quick Variable Selection Method Using Maximum of Entropy

2017 Entropy  
It uses imprecise probabilities and the maximum entropy measure to select the most informative variables without setting a threshold.  ...  The main drawback is that it is always non-negative and it requires setting the information threshold to select the set of most important variables for each dataset.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/e19060247 fatcat:z5kdfbcizrh2jltsgzahfunzxi

A New Robust Classifier on Noise Domains: Bagging of Credal C4.5 Trees

Joaquín Abellán, Javier G. Castellano, Carlos J. Mantas
2017 Complexity  
One of them is the application of bagging scheme on weak single classifiers.  ...  The Credal C4.5 (CC4.5) model is a new classification tree procedure based on the classical C4.5 algorithm and imprecise probabilities. It represents a type of the so-called credal trees.  ...  The procedure to build CDTs uses the maximum of entropy function on the above defined credal set.  ... 
doi:10.1155/2017/9023970 fatcat:ijjbvxp63bcp3jl5cjg2tndeee
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