Comparison of Data Mining Techniques for Insurance Claim Prediction

Decision tree algorithms, as the name suggests, are algorithms that can be represented graphically by a tree with many branches and leaves. Instances are classified going down from the root to the leaf nodes [WKRQ⁺08]. The nodes in the tree are tests for specific attributes. The leaves contain the predictions for the response variable.
Trees can be used for both classification and regression problems. In a classification tree the predicted value is one of the possible levels of the response variable.
The Tree construction may be seen as a variable selection method [GE03]; at each node the issue is to select the variable to divide upon and how to perform the split.
Decision tree algorithms differ in fact from the method of selecting the attribute used to test the instances at each node.
The attribute that alone classifies best the data is used at the root, then descending the tree the second best attribute is used to split further the data and so on.
The term Entropy is used to measure the \impurity" of the training dataset and can be computed for binary classification problem as well as for classification with the target attribute taking more levels. If for each node i of a classification tree, the probability of the instance to belong to the k class is pik, the entropy is then calculated as Σ P piklog pik.
The reduction of entropy can be itself a measure of the information gained partitioning on an attribute [VR02b].

Given a tree, to predict a new instances the classification begins at the root and the instance go down the tree testing different attributes until a leaf is reached. In general a decision tree model works well when:
-Each attribute of the dataset takes a small number of different levels.
-Learning rules do not overlap.

When the tree algorithm is applied, some common issues are the size of the tree, how to handle missing values/outliers and the appropriate attribute selection at each node.
Noise in the data can easily lead to an over fitted tree on the training set giving a model that does not perform well in the test set. The size determines the complexity of the tree and has to be neither too simple or too big leading to over fitting.
In order to avoid over fitting classical approaches are:
-Stop growing approaches.
-Post-pruning approaches.
In general, post pruning approaches have been preferred since it may be difficult to detect when to stop the tree growing. Regardless of the method used to avoid over fitting,the most important thing is to the determine the correct final size of the tree. There are many ways to get the correct tree size, including the use of a separate set to determine when the further split improves the model and the use of a measure of complexity. The use of a separate set to compute the correct size consists in considering each node in the tree as a candidate for pruning. Whenever the tree applied in the test set performs worse than the original give by the training set, the node is removed and it becomes a leaf.
The accuracy of the model applied to the test set increases with the proceeding of pruning.