title: Orange information score maximum value, in the context of bayesian and tree classifiers
body: <p>I am working with the Orange package and have written the following code based on the tutorials available:  </p>
  
  <pre><code>import orange,orngTest,orngStat,orngTree,Orange
  bayes = orange.BayesLearner()
  tree=orngTree.TreeLearner(mForPruning=2)
  bayes.name="bayes"
  tree.name="tree"
  data = Orange.data.Table("iris.tab")
  learners=[bayes,tree]
  results=orngTest.crossValidation(learners,data,folds=10)
  print "Learner    CA    IS    Brier    AUC"
  for i in range(len(learners)):
      print "%-8s    %5.3f    %5.3f    %5.3f    %5.3f" %\
      (learners[i].name,\
      orngStat.CA(results)[i],\
      orngStat.IS(results)[i],\
      orngStat.BrierScore(results)[i],\
      orngStat.AUC(results)[i])
  </code></pre>
  
  <p>This results in the following print:  </p>
  
  <pre><code>Running script:
  Learner      CA        IS     Brier    AUC  
  bayes       0.920    1.402    0.098    0.993  
  tree        0.940    1.447    0.120    0.967  
  </code></pre>
  
  <p>Based on the following description of <a href="http://link.springer.com/article/10.1007/BF00153760" rel="nofollow">Information Score</a>   </p>
  
  <blockquote>
    <p>Let the correct class of an instance be C. Recall that P(C) is the
    prior probability of class  C and P'(C) is the posterior probability
    returned by the classifier. We consider two cases:  (a) P'(C) > P(C) 
    Here the probability of class C has changed in the right direction,
    therefore we will  call such an answer useful. It should be awarded a
    positive score.  Co) P'(C) &lt; P(C)  Here the probability of class C has
    changed in the wrong direction, therefore we will  call such an answer
    misleading. It should be assigned a negative score.</p>
  </blockquote>
  
  <p>Following:  </p>
  
  <pre><code>Suppose the classifier in 1950 answered:   
  P'(Bush) = 0.45   
  P'(Dukakis) = 0.55   
  P'(all others) = 0  
  </code></pre>
  
  <p>Is a value greater than 1.0 invalid for information score?  Or is it the case that I have used the incorrect classifier on this type of data set, there are three distinct categories of data in the <code>iris.tab</code> data set.</p>