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1 Using Bayesian Network for combining classifiers Leonardo Nogueira Matos Departamento de Computação Universidade Federal de Sergipe

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2 Agenda Why combining classifiers? Bayesian network principles Bayesian network as an ensemble of classifiers Experimental results Future works and conclusions

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3 Why combining classifiers? Classifiers can colabore with each other Minimizes computational effort for training Maximizes global recognition rate

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4 Why not to do so? Because combining individual preditions can be so difficult as divising a robust single classifier

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5 Why not to do so? Because combining individual preditions can be so difficult as divising a robust single classifier Decision Classifiers Combiner

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6 Approaches for combining classifiers L1. Data LevelL3. Decision Level L2. Feature Level Fixed rules Trainable rules

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7 Approaches for combining classifiers L1. Data LevelL3. Decision Level L2. Feature Level Fixed rules Trainable rules

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8 Why not to do so? Because combining individual preditions can be so difficult as divising a robust single classifier Decision Classifiers Combiner p(w|x)

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9 Approaches for combining classifiers L1. Data LevelL3. Decision Level L2. Feature Level Fixed rules Trainable rules

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10 Existent scenarios Pattern space Pattern 2 1 classifiers

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11 Our scenery Pattern space classifiers

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12 A closed look

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13 A closed look – discriminant function

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14 A closed look – using multiple classifiers

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15 A closed look – using multiple classifiers The challegers: How can we combine classifier's output? How can we identify regions in pattern space?

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16 Agenda Why combining classifiers? Bayesian network principles Bayesian network as an ensemble of classifiers Experimental results Future works and conclusions

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17 Bayesian network principles A B C Those circles represent binary random variables

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18 Bayesian network principles A B C Those circles represent binary random variables

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19 Bayesian network principles A B C Those circles represent binary random variables dataset

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20 Bayesian network principles A B C Those circles represent binary random variables instance

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21 Bayesian network principles A B C Jointly probability inference is a combinatorial problem 2 possibilities 4 possibilities

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22 Bayesian network principles A B C Jointly probability inference is a combinatorial problem Independence makes computation a little more simple

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23 Bayesian network principles A B C Arest – indicates statistical dependence between variables

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24 Bayesian network principles A B C Arc – represents causality

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25 Bayesian network principles A B C A Bayesian network is a DAG (Direct Aciclic Graph) where nodes represent random variables and arcs represent causality relatioship

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26 Bayesian network principles A B C There are polinomial time algorithms to compute inference in BN

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27 Bayesian network principles A B C There are polinomial time algorithms to compute inference in BN Evidence

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28 Bayesian network principles A B C There are polinomial time algorithms to compute inference in BN Evidence messages

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29 Bayesian network principles A B C There are polinomial time algorithms to compute inference in BN Evidence

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30 Agenda Why combining classifiers? Bayesian network principles Bayesian network as an ensemble of classifiers Experimental results Future works and conclusions

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31 A Fundamental Goal

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32 Another insight From a statistical point-of-view a Bayesian network is also a graphical model to represents a complex and factored probability distribution function

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33 Another insight From a statistical point-of-view a Bayesian network is also a graphical model to represents a complex and factored probability distribution function

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34 Another insight From a statistical point-of-view a Bayesian network is also a graphical model to represents a complex and factored probability distribution function The challegers: How can we combine classifier's output? How can we identify regions in pattern space?

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35 How can we combine classifier's output? We use a BN as a graphical model of the pdf P(w|x) We assume that classifier participate in computing that function Each classifier must be a statistical classifier

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36 How can we identify regions in pattern space?

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37 Splitting pattern space

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38 Defining a region

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39 Patterns in a region

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40 Algorithm

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41 Bayesian Network Structure

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42 Bayesian networks for combining classifiers

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43 Agenda Why combining classifiers? Bayesian network principles Bayesian network as an ensemble of classifiers Experimental results Future works and conclusions

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44 Results with UCI databases

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45 Results with NIST database

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46 System I classifiers

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47 Preliminaries

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48 Results with the complete dataset

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49 Agenda Why combining classifiers? Bayesian network principles Bayesian network as an ensemble of classifiers Experimental results Future works and conclusions

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50 Future works

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51 Future works

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52 Future works

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53 Future works

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54 Future works Pattern space Pattern 2 1 classifiers

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55 Conclusions We have developed a method for combining classifiers using a Bayesian network A BN act as trainable ensemble of statistical classifiers The method is not suitable for small size dataset Experimental results reveal a good performance with a large dataset As a future work we intend to use a similar approach for splitting the feature vector and combine classifiers specialized on each piece of it.

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56 Thank you! lnmatos@ufs.br

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