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Fig. 12.2
Decision tree with the partitioning induced by it. The bold capital letters in the
partitioning denote the positive examples, the lowercase letters the negative examples. m/M
denotes a male, f/F denotes a female. The grey background denotes regions where the major-
ity class is
−
. The discrimination of the tree is 20%.
too much the males from the females. In that way we can guide the iterative tree
refinement procedure, disallowing steps that would increase discrimination in the
predictions or explicitly adding a penalty term for increasing discrimination into the
quality scores of the splits.
12.3.2.2
Related Approaches
Also for other learning algorithms a similar approach could be applied by embed-
ding the anti-discrimination constraints deeply into the learning algorithm. Another
example of such an approach is described in Chapter 14 of this topic, where a Naıve
Bayes model is learnt which explicitly models the effect of the discrimination. By
learning the most probable model that leads to the observed data, under the as-
sumption that discrimination took place, one can reverse-engineer the effect of the
discrimination and hence filter it out when making predictions.
12.3.3
Post-Processing the Induced Models
Our third and last type of discrimination-aware techniques is based upon the mod-
ification of the post-processing phase of the learnt model. We discuss the decision
tree leaf relabeling approach of (Kamiran et al., 2010b) where we assume that a tree
is already given and the goal is to reduce the discrimination of the tree by changing
the class labels of some of the leaves.
12.3.3.1
Decision Tree Leaf Relabeling
The rationale behind this approach is as follows. A decision tree partitions the space
of instances into non-overlapping regions. See, for example, Figure 12.2. In this
figure (left) a fictitious decision tree with 3 leaves is given, labeled
l
1
to
l
3
. The right
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