On the Measurement of Privacy as an Attacker's Estimation Error

A wide variety of privacy metrics have been proposed in the literature to evaluate the level of protection offered by privacy enhancing-technologies. Most of these metrics are specific to concrete systems and adversarial models, and are difficult to generalize or translate to other contexts. Furthermore, a better understanding of the relationships between the different privacy metrics is needed to enable more grounded and systematic approach to measuring privacy, as well as to assist systems designers in selecting the most appropriate metric for a given application. In this work we propose a theoretical framework for privacy-preserving systems, endowed with a general definition of privacy in terms of the estimation error incurred by an attacker who aims to disclose the private information that the system is designed to conceal. We show that our framework permits interpreting and comparing a number of well-known metrics under a common perspective. The arguments behind these interpretations are based on fundamental results related to the theories of information, probability and Bayes decision.Comment: This paper has 18 pages and 17 figure

Machine learning methods based on probabilistic decision tree under the multi-valued preference environment

In the classification calculation, the data are sometimes not unique and there are different values and probabilities. Then, it is meaningful to develop the appropriate methods to make classification decision. To solve this issue, this paper proposes the machine learning methods based on a probabilistic decision tree (DT) under the multi-valued preference environment and the probabilistic multi-valued preference environment respectively for the different classification aims. First, this paper develops a data pre-processing method to deal with the weight and quantity matching under the multi-valued preference environment. In this method, we use the least common multiple and weight assignments to balance the probability of each preference. Then, based on the training data, this paper introduces the entropy method to further optimize the DT model under the multi-valued preference environment. After that, the corresponding calculation rules and probability classifications are given. In addition, considering the different numbers and probabilities of the preferences, this paper also uses the entropy method to develop the DT model under the probabilistic multi-valued preference environment. Furthermore, the calculation rules and probability classifications are similarly derived. At last, we demonstrate the feasibility of the machine learning methods and the DT models under the above two preference environments based on the illustrated examples