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Thus, if there are q classes and p attribute values, the goal is to compute p x q matrices S^^ S^ where the sum of corresponding entries sf^-\- sf^ gives the probabiHty estimate for class Q given that the attribute has value a/. A single probability estimate su can be computed as follows: Pd constructs a binary vector corresponding to the entities in the training set with 1 for each item having the value ai and 0 for other items. Pc constructs a similar vector with l/ui for the n^ entities in the class, and 0 for other entities.

Thus, the entire tree represents a disjunction of conjunctions of constraints on the attribute-values of instances. This tree can also be represented as a set of if-then rules. This adds to the readabihty and intuitiveness of the model. 1. 1 shows one possible decision tree learned from this data set. New instances are classified by sorting them down the tree from the root node to some leaf node, which provides the classification of the instance. Every interior node of the 32 Predictive Modeling for Classification tree specifies a test of some attribute for the instance; each branch descending from that node corresponds to one of the possible values for this attribute.

With horizontally partitioned data, the developed model can be given to all sites, and any party can locally classify a new instance. With vertically partitioned data, the problem is more complex. 3), the root site first makes a decision based on its data. It then looks at the node this decision leads to and tells the site responsible for that node the node and the instance to be classified. This continues until a leaf is reached, and which point the site that originally held the class value knows the predicted class of the new instance.

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