subject to the condition that d k=1 ak = 1. This property is a special case of a more general theorem involving convex functions (which include the logarithmic function) known as Jensen’s inequality.

By applying Jensen’s inequality, Equation 4.4 can be bounded as follows:




Because E(Y |X) ? E(Y ) ? 0, it follows that entropy never increases after

splitting on an attribute.

Computer Science & Information Technology

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