Understanding privacy risk of publishing decision trees

Publishing decision trees can provide enormous benefits to the society. Meanwhile, it is widely believed that publishing decision trees can pose a potential risk to privacy. However, there is not much investigation on the privacy consequence of publishing decision trees. To understand this problem, we need to quantitatively measure privacy risk. Based on the well-established maximum entropy theory, we have developed a systematic method to quantify privacy risks when decision trees are published. Our method converts the knowledge embedded in decision trees into equations and inequalities (called constraints), and then uses nonlinear programming tool to conduct maximum entropy estimate. The estimate results are then used to quantify privacy. We have conducted experiments to evaluate the effectiveness and performance of our method.