Differential Privacy

Question:

Write an essay on Differential Privacy.

Answer:

“Differential Privacy” is a term that is being used mainly in the statistical database. The particular privacy is actually a cryptograph that helps in maximizing the accuracy that are there and at the same time it helps in minimizing the queries that are there (Shao, Jiang, Kister, Bressan and Tan 2013). Statistical database helps in keeping the statistical information about a particular population in a computed form. The particular setting helps in revealing the information that is there in the database, but then along with the information of the population the privacy of the population is revealed as well. 

The privacy preservation of the analysis had to face the problem of keeping the information of public private. The problem is one of the general problem and thus in the year 1977, Dalenius, came up with the “semantic security”. The particular term is defined, almost five years later, Goldwasser and Micali. According to these people, the particular term referred to crypto system and this particular thing enables anyone to keep the information of the population private. According to the definition of these two men, people could have an access to the information about a particular population through the statistical system. One can understand this particular thing in a very simple way. For instance, a statistical database contains information about the heights of the women in a particular country. Now the information that is there in the statistical database required but then if the information regarding a woman’s height is revealed then there will be a breach of privacy (Chatzikokolakis, Andrés, Bordenabe and Palamidessi 2013). Therefore, the database would provide the average heights of the women in the nation, without revealing the height of a single woman. The information that a person, who is having an access to the statistical database, is relatively more than that person who is not having an access to the statistical database of each individual. Differential privacy tries to capture those semantic securities of crypto system that are not captured by the relaxed version for the semantic security. 

In the recent years there has been a growing concern regarding the data privacy that is there in the social network. The social network contains graphs and other valuable information, regarding a particular thing. The information is useful for the researchers but then this is not all good for the individuals; since it breach the notion of privacy (Andrés, Bordenabe, Chatzikokolakis and Palamidessi 2013). Differential privacy is a kind of data mining that helps in hiding the presence of the individuals in a data set. The differential privacy although, hides the data, yet it provides a strong mathematical guarantee at the same time. The differential privacy actually use the noises to hides the individual data, but then it does not in any way provides wrong statistical information about a particular thing, thus, it is being considered as a safe way for data mining. In spite of the fact that the differential privacy is important in keeping the privacy of the data in the social networks, many of the social scientists do not use it. One of the most important reasons behind not using is the fact that this particular system is very complex in nature. Therefore, in order to escape those complexities many social scientists still use simple anonymities for preserving the data. 

Comprehensive survey and analysis of differential privacy in social network data publication

The differential privacy is something that has revolutionized the field of privacy preservation data mining analysis (Ghosh, Roughgarden and Sundararajan 2012). One of the main reasons behind this revolution is the fact that there has been an inclusion of the noise in the answers as well as in the queries of the people. Therefore, it has helped in hiding the identity of the individuals and thus it has helped in protecting the privacy of the individuals at the same time. The particular process of differentiation, although face criticism as well (Lantz, Boyd and Page 2015). The particular process of data mining face criticism because, of the syntactical anonymity; while, it is true that at the time of using differential privacy syntactical anonymity could cause problem, it is also true that such problems could be solved easily within the framework only. 

The problem of syntactical anonymity can be seen as a drawback that could be violating the legitimate utility of the sanitization. The sanitization has been used with the goal of not using or rather not revealing the sensitive individual data for any purpose. Therefore, the process of anonymity is used for sanitization of the data. The process of anonymization is at least a way to sanitize the data that are available for any kind of research. It is true that when there is a sanitization of the data then the process of the data analysis will not get much support from the researcher (Clifton and Tassa 2016). Thus, it could affect the result of the research and thus could affect adversely to the research at the same time. Therefore, many times the social scientist accepts the process of not using the sanitization, and thus shares the privacy of the individual. Therefore, this particular process may help in providing a great support to the data analysis process, but then there is a risk attached to it because of the individual information being shared. Thus, the particular problem places the social scientist and the researchers in difficult situation where, they only have two choices in front of them. Both the choices some kind of adversity attached to it, one way or other has to be compromise in case of any data analysis, if the process of legitimate sanitization is followed.

The differential privacy although had many utilities, and helps in sanitization of the data without compromising the data analysis part, yet there are few social scientists, who does not accept this particular method. The reason behind the non-acceptance of the particular method is the fact that most of the researchers could not accept adding noises to the data. The syntactical model that is being used by the social researchers and the differential privacy model, along with those models where there is the addition of the noises, have certain points of differences (Wang, Chow, Wang, Ren and Lou 2013). The points of differences are based on the certain grounds and these are the following:

Ground Syntactical Model Differential Privacy Model/Noise Added Models

Privacy Policy Management The syntactical model has a distinct and a clear relationship with the legitimate concept of individual identifiable data (Clifton and Tassa 2016). The particular model has data schema and parameters that are independent of the actual data. The e difference privacy model, although, has a relationship with the individual identifiable parameter, the relationship with the privacy parameters are not clear in this concept. In case of e, differential privacy there should be the extensive analysis of the universe, data as well as the query. Thus, it can be said that for the e differential privacy no general privacy for value is sufficient.

Open Ended compared to the Compact Distribution In case of the Syntactical model, for the given anonymized data value the process of compact distribution is used. The compact distribution of the data ensures that there will be accuracy. In case of the noise-based models such as the Perturbation-based model, such is not the case. In this particular model, open-ended data are used. The open-ended distribution therefore, is probabilistic in nature. Thus, even if it provides tighter bound the analysis it receives is not the one that is being desired by the researchers. Thus, it is again another reason why the practitioners do not want to use those methods that include noise addition

One should remember the fact that in case of any research he/she could use more than one or multiple queries, in case of a research and that would not violate any privacy in any way. Thus, in case of differential privacy, the answers that are received against each query are composable and thus, the queries forms the part of the “privacy budget”. The particular thing can be understand with the help of a particular example (Fan and Jin 2016). According to this particular example, to achieve the e differential privacy it is important have e differential privacy over the two queries. In order to do that it is important to make the queries nosier.

If one goes by the basic definition of the differential practices then the probability that is there for the noisy outcomes, also account for the multi-dimensional outcomes that are there (Task 2016). Thus, addition noise is an important factor in case of differential privacy, although it is not everything in case of differential privacy. In case of differential privacy in social network data publication, it is important to correlate the attributes.

Therefore, e differential privacy is something that generates not only, independent privacy but at the same time, it is a rigorous method of privacy (Dwork and Roth 2014). In case of applying the differential privacy in the network data one may face a problem because most of the time the network data are inherently correlated. In case of correlating settings, the differential privacy faces failure because it could not guarantee privacy.

There are many researchers who have used the differential privacy to publish the social network data, and at the same time had ensured and guaranteed privacy. The things that they used to publish the social network data include the extraction of the detailed structure. Along with the extraction of the detailed structured into the degree of the correlation of the statistics, the noises are introduced by the researchers at the same time (Zheleva, Terzi and Getoor 2016). Along with the noises and the detailed structures in the statistics, the researchers could publish data in the social network, which had not violated the privacy as well. Many other researchers argue that the use of the differential privacy is not possible in the real world.

In case of the risk based privacy definition and the differential privacy there lays a difference. The difference is that in case of the risk-based privacy, to analyze the set sized value, and the anonymity has used the fixed amount of noise in case of the e differential (Andrés, Bordenabe, Chatzikokolakis and Palamidessi 2013). In case of the differential privacy, although, noises are being added to all the records in the database; thus, the data receives a primary protection from it, and these are the main differences between risk-based differential and the differential privacy.

The research on the differential privacy started during the middle of the decade and although it has differences with the syntactic anonymity, the particular method is based on syntactical-anonymity at the same time (Chung, Shafiee and Wong 2016). A greater part of the academic community has accepted this particular approach because of two reasons. Among, these two reasons, one is that this particular approach is a rigorous approach. The second and the most important reason is that this particular approach is about guarantying privacy of the individual involved in the data collection as well as in the data analysis method.

Apart from this particular reason, there is also another reason behind adapting this particular method of privacy and that is in case there is any attacker, then it will, act as a proof against that attacker. It could be used as a proof because the background of the knowledge that will be there is very strong in nature. In case of differential privacy, if there is a strong attacker then that attacker has the knowledge of all queries. It is true that the strong attacker has the knowledge of all the queries, but at the same time, it is also true that the strong attackers could not violate the privacy at the same time (Peressutti, Bai, Jackson, Sohal, Rinaldi, Rueckert and King 2015). Therefore, the result of the query would indistinguishable whether or not the record was there in the data. Another important breakthrough of the particular method is the addition of the noise in the method. The addition of the noise, to the continuous-valued privacy resulted in coming up with a measure that would provide composable query. The composable query thus helped or rather provided support in case of the multiple data or query. Thus, the differential privacy in the last decades became one of the most important tools for the researchers that helped them to maintain and guarantees privacy.

In the recent days, the acceptance of the differential privacy has increased largely, and this took place because the particular method guarantees robust privacy, in case of protecting the sensitive data. In case of publishing data in the social networks, one has to keep two things in mind. The first requirement includes maintaining the utility of the original data that are there. The data analysis of the social network depends on the eigenvectors that are there in the top of the adjacency matrices (Wang, Song, Lou and Hou 2015). The measurement of the utility will be based on the top eigenvectors of the published data to the eigenvectors of the original data. 

The second requirement includes guarantying the desired privacy, and that includes the opponent learning nothing more about the published data that are there. Most of the academicians and the social scientists are of the opinion that both these requirements are conflicting requirements. If one has to meet these two requirements then it is important to add large amount of noises to the query. The process may help in hiding the individual data and in protecting the privacy of the individual but then this particular process will come up with lots of mistakes, while it is approximating the top eigenvectors of the original data. In case of database, it is important to have the best tradeoffs of both the privacy as well as the utility.

Therefore, some social scientists have used the random matrix theory along with the differential privacy theory, to overcome the shortcomings. The first thing that is to be done in case of the random matrix is to project each row of the adjacency matrix with low dimensional space. One should carry out the projection of each row with the help of the random matrix and at the same time, there should be the perturbation of the whole matrix with the help of the random noise. 

The result of using this particular method is that this particular method, the dimensionality of using the matrix is lowered and at the same time the publishing dense matrixes are being avoided at the same time. The second critical approach of this particular theory helps in preserving the top eigenvectors of the adjacency matrix. Third important critical approach of using this particular theory states that the random projection helps in achieving differential privacy. If this particular theory is being used then it is possible to ensure that differential privacy is introduced in the second step, provided there is the introduction of the random perturbation (Ahmed, Jin and Liu 2016). The random perturbation that will be introduced should be “small” and only if a “small” random perturbation is used, one can ensure to introduce differential privacy in the second step.

In case of online publication of the social network data, it is important to use the random projection theory as that will help in reducing the noise that is being used in differential privacy. The nodes that are used in the online sites are in millions and billions number; therefore, the social scientists have to conceptualize both the cost as well as the storage space. In case of using random projection method, the social scientists as well as the researchers are beneficial in more than one way (Hilton 2016). Firstly, the reduction of the dimensionality helps in reducing the computational cost that is required for algorithm. Secondly, the addition of the small amount of noise helps in maintaining the utility of the data. Most importantly, if random projections are used in case of online publication of the social network data then that will help achieving differential privacy.

In case of publishing social network data, it is important to publish the graph, or the differential private graph, that contains data. The social network data should have the publication of the graph but it should not, violate the differential privacy. In other words, it should try to protect the privacy of the individual. Most of the time, in case of the publication of the social network graphs, the social scientists have used the perturbing Kronecker model and its parameter (Lee and Nedic 2013). Therefore, for this reason the researchers have developed the differential private algorithm. The particular algorithm helps in preserving any of the two samples that are there in the database set. The use of the particular method or the model has one important drawback (Fontugne, Abry, Fukuda, Borgnat, Mazel, Wendt and Veitch 2015). The drawback of this particular model is that it may deals with the differential private publication of  the data in the database; but then, they do not addresses the utility of preserving the eigenvectors, which forms the part of the graph.  The preservation of the eigenvectors is one of the central themes of the work.

Therefore, in the present day, in case of the publication of the data in the social network several algorithms are being proposed (Grellmann, Neumann, Bitzer, Kovacs, Tönjes, Westlye, Andreassen, Stumvoll, Villringe and Horstmann 2016). The proposed algorithms help in preserving the differential private copy of the top eigenvectors, to the original data sets that are there. One of the suggested algorithms includes using the covariance matrix. In this particular matrix the original data that are there in tainted by the addition of the random noise (Hilton 2016).

The use of the random projection could help in publishing the social network graph, without affecting the utility and the differential privacy of the data. In case of the random projection, both differential privacy and the Eigen spectrum of the matrix that is being provided can be preserved. The particular thing could only be done, if there are some modifications in the original matrix that is there. The researchers and the social scientists are of the opinion that in case of the publication of the social network data, the randomized approach should be used. The randomized approached helps in inverting certain featured attributes of the data. The inversion of the featured attributes takes place with the help of the fixed probabilities that are being used. The particular approach has one drawback, which is why it could not be used in the social network data analysis. The one major drawback that is there is the fact this particular approach has a high demand in case of both computations as well as in case of storage space at the same time. The approaches that are being used in this case should generate large dense matrix. The large dense matrix that should be generating could be generated either implicitly or explicitly. The large size that should be generated should be of n X n sizes. The “n” here refers to number of users that are there in a particular network. Therefore, in case of 10 million users the manipulation of the matrix size should be of 1014.  Therefore, the storage size that is required in this particular case is of few pet bytes. In case the users are not having more than 100 links, then the graph in the social network could be represented by a sparse graph. The particular process consumes only few gigabytes of the memory. One should keep in mind that in the case of differential privacy, the desired knowledge should be incorporate in the algorithm.

In case of publication of the social network data or in case of data mining there has been the application of many techniques. There are many surveys, which provide lots of comprehensive review. Several examples can be derived from the comprehensive reviews. Among those several examples, one includes the application of the differential privacy for releasing query and for click histograms. The histograms are click from publishing commuting patterns, search logs, and even from the publishing result of the machine pattern.

The recent works of differential privacy depends mainly on the count query. In case of publishing the count queries, many researchers have suggested to use the hierarchy of intervals. According to few other groups of researchers, suggest using a general framework for publishing of the count queries.  The general framework should have the support of the answers that are there in the given workload of the count queries. Along with it, the general framework should support the optimal strategy of the given workload of the count queries.

There are approaches that ensure that it is possible to publish set of marginal of a particular contingency table, by ensuring the differential privacy, and this is possible with the help of the noise addition only. Many researchers use the wavelet approach to range the count queries. There is the extension of the wavelet approach towards the nominal attributes and multi-dimensional count queries. In case of the multi-dimensional count queries the study regarding the problem of publishing data cubes, keeps two things in account. First, is that it ensures the differential privacy and at the same time, it ensures variance of noise for the purpose of better utility. 

The differential privacy is mainly depended on the two kinds of policies; between the two kinds of policies, one is gaining precision over the discovered location. The second policy is related to the output counts that are associated with these locations (Ji and Elkan 2013). Differential privacy makes sure that the ability of the adversary is essentially the same and at the same time, it is independent, even if anyone of the individual opts out of the data set. In case there is an opting out of a user, from the location of the history that is there in the database, then the changes that will be there will be very interesting in nature. The change would only be interesting if the adversary could detect the change that is occurring.

In case of the use of the previous privacy mechanism, it is not possible for the data to work well, although, it could ensure privacy at the same time. The data are not working in this case because the noise that is being added in this case is Laplace noises.

The application of the differential privacy is there on the disparate data sets as well as the applications. The location pattern of the mining data set helps in presenting an algorithm for differential privacy. The algorithm helps in overcoming the location-mining pattern output helps in overcoming the output. The thing is done by identifying two important issues and among those two important; one that is most important is related to the controlling magnitude of the sensitivity. It is important to control magnitude of sensitivity, because it is one of the critical things for the Laplace noise perturbation. The second thing that is being identified includes, identifying desired differential privacy to achieve the applied or the practical differential privacy. 

The publication of the social network data is a very crucial process and that must be done in a secured manner so that the privacy concern of the users cannot be hampered. Differential privacy has played a significant role in case of the social network data publication (News.psu.edu. 2016). However, there are also few drawbacks of the differential privacy in this particular process. The process of protecting privacy of people in the era of online big data is not easy. However, the protection of people’s privacy through the publication of social network data while utilizing the visual representations of such things as the data of social network may available authentic challenges (Dwork 2016). 

The privacy issue is such a challenge that is related to the balancing personal data protection against the global statistics advantages as public goods. Differential privacy is mainly required for maximizing the analysis accuracy during the prevention of the individual record identification (McSherry and Talwar 2015). Huge databases such as those of the United States Bureau contain data that while analyzed as well as aggregated, can make an illumination of the health, economic and social problems and solutions as well (Mironov et al., 2012). Nevertheless, the privacy protection needs more than simply the removal of the recognizing data from the files before publishing analytic results and databases. Data can be correlated easily among the databases with the multiple numbers of open public databases available for pulling together pieces and bits of deleted data as well as recovering the recognizing information (Friedman and Schuster 2012). 

The owners of database intended to be capable of predicting what people intended to view so that they fix a competition for developing the best learning and the most informative algorithms for the real data. The database owners had the thought that eliminating the recognizing information made it safe for publishing the database (Dwork 2012). Nevertheless, while visualizing the patterns from the paid service were distinguished to viewing patterns on the self-reporting, public movie-viewing database, sufficient information was there for identifying an overwhelming majority of the individuals who are involved in this process (Xiao, Wang and Gehrke 2012). On the other hand, same kinds of problems can also be encountered with the histories of search engine as well as other databases as it is not sufficient for just stripping the obvious recognizing information (Dwork and Lei 2014). One approach to achieve the differential privacy is integrating a small amount of noise towards the exact statistics before publishing them. An issue in this process is the figuring out the quantity of noise that it mainly depends on how much sensitive the statistics is and how for doing it so that people still can retain the result’s accuracy (Li et al., 2015). Therefore, there are some other more sophisticated as well as applicable approaches in order to achieve the a proper differential privacy in case of publication of the social network data. Most importantly, the notion of the differential privacy in case of the social network data can be especially essential towards the protection of the graph data (Dwork et al., 2016). 

Conclusion

Therefore, it can be concluded that the data that are there are important for the social scientists as well as for the research area. Therefore, it is important to publish the data because it will help the other researches and the other research areas. Thus, publication of the social network data is an important thing but if there is the publication of the social network data then it could actually be harmful for the individuals as well. There are certain data, which are very sensitive, and thus it could harm the individuals at the same time. Thus, today the privacy issue has become one of the most important issues, for the social scientists and it is important to protect individual data, especially those data that are sensitive. There are many ways to protect the data, and among those many, one is using noises to hide the individuals. The method, where the noises are being used, is known as the differential privacy. The differential privacy is there in the use since the last decade. Many researchers have used it but there are few, who, have not and they have not used this particular method because they do not want to use such a method where there is the addition of the noises. The methods where there has been the addition of the noises had affected the research in more than one way previously. Therefore, the researchers have thought that differential privacy will not be an exception.

It is true that there are certain drawbacks of this particular method, and among those, one is related to the syntactical anonymity. The error or the drawback related to syntactical anonymity is not something that is a major drawback. The particular drawback could be easily be reformed, by staying within the framework. Thus, even if there are drawbacks then also it could be used because there are different other alternatives that could be implemented in it, which could help in overcoming the drawback. Thus, in the differential privacy random projection could be used, this will again help in improving the method, and at the same time, it will help in reducing the privacy cost and the storage space as well.

The differential privacy is a mechanism that is considered as considerably new mechanism that has been introduced for the researchers. The researchers are of the opinion that in the coming years the particular mechanism will become a strong and a powerful mechanism. The reason behind calling it a powerful and a strong mechanism is the fact that in the coming years there will be a growth in the number as well as in the volume of database. The researchers who are using the differential privacy too, should keep this thing in mind that this particular tool is an important tool that helps in protecting the data. Therefore, the researchers should properly utilize the data and should protect the data of the individuals in a particular dataset. The researchers, with the help of the, differential privacy could take the advantage of the privacy guarantee with the help of the privacy guarantees.

The researchers and the social scientists are of the opinion that the differential policy is an important and a very useful weapon. The weapon is useful and important that will help guarantying privacy but at the same time it is also true that this particular thing is not universal in nature. The syntactical anonymity is something that is still acceptable by many researchers because it provides the true value to the researchers. It is true although that this particular method, actually reduces the privacy, yet according to some critics and researchers’ people use it to gain true value of the data. In case of the differential privacy, such is not the case, because in case of differential privacy, the result that is being obtained is very far from the result that is being obtained from the data.

It is true that in order to maintain privacy the differential privacy mechanism can be used but then it is true as well, that there are some drawbacks of this particular mechanism. Moreover, at the same time it is true as well, that there are many facts that are not known about this particular method. Thus, further research has to be made to know more about this particular mechanism. In further research, the facts that will be derived will help in finding out the solutions to the loop holes that are there in the particular mechanism.?

References

Ahmed, F., Jin, R. and Liu, A. (2016). A Random Matrix Approach to Differential Privacy and Structure Preserved Social Network Graph Publishing. 1st ed.

Andrés, M.E., Bordenabe, N.E., Chatzikokolakis, K. and Palamidessi, C., 2013, November. Geo-indistinguishability: Differential privacy for location-based systems. In Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security (pp. 901-914). ACM.

Andrés, M.E., Bordenabe, N.E., Chatzikokolakis, K. and Palamidessi, C., 2013, November. Geo-indistinguishability: Differential privacy for location-based systems. In Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security (pp. 901-914). ACM.

Chatzikokolakis, K., Andrés, M.E., Bordenabe, N.E. and Palamidessi, C., 2013, July. Broadening the Scope of Differential Privacy Using Metrics. InPrivacy Enhancing Technologies (pp. 82-102).

Chung, A.G., Shafiee, M.J. and Wong, A., 2016. Random Feature Maps via a Layered Random Projection (LaRP) Framework for Object Classification.arXiv preprint arXiv:1602.01818.

Clifton, C. and Tassa, T. (2016). On Syntactic Anonymity and Differential Privacy. 1st ed.

Dwork, C. and Lei, J., 2014, May. Differential privacy and robust statistics. In Proceedings of the forty-first annual ACM symposium on Theory of computing (pp. 371-380). ACM.

Dwork, C. and Roth, A., 2014. The algorithmic foundations of differential privacy. Foundations and Trends in Theoretical Computer Science, 9(3-4), pp.211-407.

Dwork, C., 2012. Differential privacy: A survey of results. In Theory and applications of models of computation (pp. 1-19). Springer Berlin Heidelberg.

Dwork, C., 2016. Differential privacy. In Automata, languages and programming (pp. 1-12). Springer Berlin Heidelberg.

Dwork, C., Naor, M., Pitassi, T. and Rothblum, G.N., 2016, June. Differential privacy under continual observation. In Proceedings of the forty-second ACM symposium on Theory of computing (pp. 715-724). ACM.

Fan, L. and Jin, H. (2016). A Practical Framework for Privacy-Preserving Data Analytics. 1st ed.

Fontugne, R., Abry, P., Fukuda, K., Borgnat, P., Mazel, J., Wendt, H. and Veitch, D., 2015, April. Random projection and multiscale wavelet leader based anomaly detection and address identification in Internet traffic. InAcoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on (pp. 5530-5534). IEEE.

Friedman, A. and Schuster, A., 2012, July. Data mining with differential privacy. In Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining (pp. 493-502). ACM.

Ghosh, A., Roughgarden, T. and Sundararajan, M., 2012. Universally utility-maximizing privacy mechanisms. SIAM Journal on Computing, 41(6), pp.1673-1693.

Grellmann, C., Neumann, J., Bitzer, S., Kovacs, P., Tönjes, A., Westlye, L.T., Andreassen, O.A., Stumvoll, M., Villringer, A. and Horstmann, A., 2016. Random Projection for fast and efficient multivariate correlation analysis of high-dimensional data: A new approach. Frontiers in Genetics, 7, p.102.

Hilton, M. (2016). Differential Privacy: A Historical Survey. 1st ed. Cal Poly State University.

Ji, Z. and Elkan, C. (2013). Differential privacy based on importance weighting. Mach Learn, 93(1), pp.163-183.

Lantz, E., Boyd, K. and Page, D., 2015, October. Subsampled Exponential Mechanism: Differential Privacy in Large Output Spaces. In Proceedings of the 8th ACM Workshop on Artificial Intelligence and Security (pp. 25-33). ACM.

Lee, S. and Nedic, A., 2013. Distributed random projection algorithm for convex optimization. Selected Topics in Signal Processing, IEEE Journal of,7(2), pp.221-229.

Li, C., Hay, M., Rastogi, V., Miklau, G. and McGregor, A., 2015, June. Optimizing linear counting queries under differential privacy. In Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems (pp. 123-134). ACM.

McSherry, F. and Talwar, K., 2015, October. Mechanism design via differential privacy. In Foundations of Computer Science, 2007. FOCS'07. 48th Annual IEEE Symposium on (pp. 94-103). IEEE.

Mironov, I., Pandey, O., Reingold, O. and Vadhan, S., 2012. Computational differential privacy. In Advances in Cryptology-CRYPTO 2009 (pp. 126-142). Springer Berlin Heidelberg.

News.psu.edu. (2016). Social network analysis privacy tackled | Penn State University. [online] Available at: http://news.psu.edu/story/344805/2015/02/14/research/social-network-analysis-privacy-tackled [Accessed 9 Jun. 2016].

Peressutti, D., Bai, W., Jackson, T., Sohal, M., Rinaldi, A., Rueckert, D. and King, A., 2015. Prospective Identification of CRT Super Responders Using a Motion Atlas and Random Projection Ensemble Learning. In Medical Image Computing and Computer-Assisted Intervention–MICCAI 2015 (pp. 493-500). Springer International Publishing.

Shao, D., Jiang, K., Kister, T., Bressan, S. and Tan, K.L., 2013, August. Publishing trajectory with differential privacy: A priori vs. a posteriori sampling mechanisms. In Database and Expert Systems Applications (pp. 357-365). Springer Berlin Heidelberg.

Task, C. (2016). "Privacy-preserving social network analysis" by Christine Task. Docs.lib.purdue.edu.

Wang, B., Song, W., Lou, W. and Hou, Y.T., 2015, April. Inverted index based multi-keyword public-key searchable encryption with strong privacy guarantee. In Computer Communications (INFOCOM), 2015 IEEE Conference on (pp. 2092-2100). IEEE.

Wang, C., Chow, S.S., Wang, Q., Ren, K. and Lou, W., 2013. Privacy-preserving public auditing for secure cloud storage. Computers, IEEE Transactions on, 62(2), pp.362-375.

Xiao, X., Wang, G. and Gehrke, J., 2012. Differential privacy via wavelet transforms. Knowledge and Data Engineering, IEEE Transactions on, 23(8), pp.1200-1214.

Yang, Y., Zhang, Z., Miklau, G., Winslett, M. and Xiao, X. (2012). Differential privacy in data publication and analysis. Proceedings of the 2012 international conference on Management of Data - SIGMOD '12.

Zheleva, E., Terzi, E. and Getoor, L. (2016). Privacy in Social Networks. 1st ed.

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