Differential Privacy on Linked Data: Theory and Implementation Yotam Aron

Table of Contents Introduction Differential Privacy for Linked Data SPIM implementation Evaluation

Contributions Theory on how to apply differential privacy to linked data. Experimental implementation of differential privacy on linked data. Overall privacy module for SPARQL queries.

Introduction

Overview: Why Privacy Risk? Statistical data can leak privacy. Mosaic Theory: Different data sources harmful when combined. Examples: Netflix Prize Data set GIC Medical Data set AOL Data logs Linked data has added ontologies and meta-data, making it even more vulnerable. Linked data has added ontologies and meta-data, making it even more vulnerable

Current Solutions Accountability: Privacy Ontologies Privacy Policies and Laws Problems: Requires agreement among parties. Does not actually prevent breaches, just a deterent. Heterogeneous

Current Solutions (Cont’d) Anonymization Delete “private” data K – anonymity (Strong Privacy Guarantee) K – anonymity Problems Deletion provides no strong guarantees Must be carried out for every data set What data should be anonymized? High computational cost (k-anonimity is np-hard)(k-anonimity is np-hard)

Differential Privacy

How Achieved? Add noise to result. Simplest: Add Laplace noise

Laplace Noise Parameters

Other Benefit of Laplace Noise

Benefits of Differential Privacy Strong Privacy Guarantee Mechanism-Based, so don’t have to mess with data. Independent of data set’s structure. Works well with for statistical analysis algorithms.

Problems with Differential Privacy Potentially poor performance Complexity (especially for non-linear functions) Noise Only works with statistical data (though this has fixes) How to calculate sensitivity of arbitrary query?

Differential Privacy for Linked Data

Differential Privacy and Linked Data Want same privacy guarantees for linked data without, but no “records.” What should be “unit of difference”? One triple All URIs related to person’s URI All links going out from person’s URI

Differential Privacy and Linked Data Want same privacy guarantees for linked data without, but no “records.” What should be “unit of difference”? One triple All URIs related to person’s URI All links going out from person’s URI

Differential Privacy and Linked Data Want same privacy guarantees for linked data without, but no “records.” What should be “unit of difference”? One triple All URIs related to person’s URI All links going out from person’s URI

Differential Privacy and Linked Data Want same privacy guarantees for linked data without, but no “records.” What should be “unit of difference”? One triple All URIs related to person’s URI All links going out from person’s URI

“Records” for Linked Data Reduce links in graph to attributes Idea: Identify individual contributions from a single individual to total answer. Find contribution that affects answer most.

“Records” for Linked Data Reduce links in graph to attributes, makes it a record. P1P2 Knows PersonKnows P1P2

“Records” for Linked Data Repeated attributes and null values allowed P1P2 Knows P3P4 Loves Knows

“Records” for Linked Data Repeated attributes and null values allowed (not good RDBMS form but makes definitions easier) PersonKnows Loves P1P2NullP4 P3P2P4Null

Query Sensitivity in Practice Need to find triples that “belong” to a person. Idea: Identify individual contributions from a single individual to total answer. Find contribution that affects answer most. Done using sorting and limiting functions in SPARQL

Example COUNT of places visited P1 P2 MA S2 S3 State of Residence S1 Visited

Example COUNT of places visited P1 P2 MA S2 S3 State of Residence S1 Visited

Example COUNT of places visited P1 P2 MA S2 S3 State of Residence S1 Visited Answer: Sensitivity of 2

Using SPARQL Query: (COUNT(?s) as ?num_places_visited) WHERE{ ?p :visited ?s }

Using SPARQL Sensitivity Calculation Query (Ideally): SELECT ?p (COUNT(ABS(?s)) as ?num_places_visited) WHERE{ ?p :visited ?s; ?p foaf:name ?n } GROUP BY ?p ORDER BY ?num_places_visited LIMIT 1

In reality… LIMIT, ORDER BY, GROUP BY doesn’t work together in 4store… For now: Don’t use LIMIT and get top answers manually. I.e. Simulate using these in python Would like to keep it on sparql-side ideally so there is less transmitted data (e.g. on large data sets)

(Side rant) 4store limitations Many operations not supported in unison E.g. cannot always filter and use “order by” for some reason Severely limits the types of queries I could use to test. May be desirable to work with a different triplestore that is more up-to-date (ARQ). Didn’t because wanted to keep code in python. Also had already written all code for 4store

Problems with this Approach Need to identify “people” in graph. Assume, for example, that URI with a foaf:name is a person and use its triples in privacy calculations. Imposes some constraints on linked data format for this to work. For future work, maybe there’s a way to automatically identify private data, maybe by using ontologies. Complexity is tied to speed of performing query over large data set.

…and on the Plus Side Model for sensitivity calculation can be expanded to arbitrary statistical functions. e.g. dot products, distance functions, etc. Relatively simple to implement using SPARQL 1.1

Differential Privacy Protocol Differential Privacy Module Client SPARQL Endpoint Scenario: Client wishes to make standard SPARQL 1.1 statistical query. Client has Ɛ “budget” of overall accuracy for all queries.

Differential Privacy Protocol Differential Privacy Module Client SPARQL Endpoint Step 1: Query and epsilon value sent to the endpoint and intercepted by the enforcement module. Query, Ɛ > 0

Differential Privacy Protocol Differential Privacy Module Client SPARQL Endpoint Step 2: The sensitivity of the query is calculated using a re-written, related query. Sens Query

Differential Privacy Protocol Differential Privacy Module Client SPARQL Endpoint Step 3: Actual query sent. Query

Differential Privacy Protocol Differential Privacy Module Client SPARQL Endpoint Step 4: Result with Laplace noise sent over. Result and Noise

Design of Privacy System

SPARQL Privacy Insurance Module i.e. SPIM Use authentication, AIR, and differential privacy in one system. Authentication to manage Ɛ-budgets. AIR to control flow of information and non-statistical data. Differential privacy for statistics. Goal: Provide a module that can integrate into SPARQL 1.1 endpoints and provide privacy.

Design Triplestore User Data Privacy Policies SPIM Main Process AIR Reasoner Differential Privacy Module HTTP Server OpenID Authentication

HTTP Server and Authentication HTTP Server: Django server that handles http requests. OpenID Authentication: Django module. HTTP Server OpenID Authentication

SPIM Main Process Controls flow of information. First checks user’s budget, then uses AIR, then performs final differentially-private query. SPIM Main Process

AIR Reasoner Performs access control by translating SPARQL queries to n3 and checking against policies. Can potentially perform more complicated operations (e.g. check user credentials) Privacy Policies AIR Reasoner

Differential Privacy Works as discussed in previous slides. Contains users and their Ɛ- values. Differential Privacy Module User Data

Evaluation

Three things to evaluate: Correctness of operation Correctness of differential privacy Runtime Used a anonymized clinical database as the test data and added fake names, social security numbers, and addresses.

Correctness of Operation Can the system do what we want? Authentication provides access control AIR restricts information and types of queries Differential privacy gives strong privacy guarantees. Can we do better?

Use Case Used in Thesis Clinical database data protection HIPAA: Federal protection of private information fields, such as name and social security number, for patients. 3 users Alice: Works in CDC, needs unhindered access Bob: Researcher that needs access to private fields (e.g. addresses) Charlie: Amateur researcher to whom HIPAA should apply Assumptions: Django is secure enough to handle “clever attacks” Users do not collude, so can allocate individual epsilon values.

Use Case Solution Overview What should happen: Dynamically apply different AIR policies at runtime. Give different epsilon-budgets. How allocated: Alice: No AIR Policy, no noise. Bob: Give access to addresses but hide all other private information fields. Epsilon budget: E1 Charlie: Hide all private information fields in accordance with HIPAA Epsilon budget: E2

Use Case Solution Overview Alice: No AIR Policy Bob: Give access to addresses but hide all other private information fields. Epsilon budget: E1 Charlie: Hide all private information fields in accordance with HIPAA Epsilon budget: E2

Example: A Clinical Database Client Accesses triplestore via HTTP server. OpenID Authentication verifies user has access to data. Finds epsilon value, HTTP Server OpenID Authentication

Example: A Clinical Database AIR reasoner checks incoming queries for HIPAA violations. Privacy policies contain HIPAA rules. Privacy Policies AIR Reasoner

Example: A Clinical Database Differential Privacy applied to statistical queries. Statistical result + noise returned to client. Differential Privacy Module

Correctness of Differential Privacy Need to test how much noise is added. Too much noise = poor results. Too little noise = no guarantee. Test: Run queries and look at sensitivity calculated vs. actual sensitivity.

How to test sensitivity? Ideally: Test noise calculation is correct Test that noise makes data still useful (e.g. by applying machine learning algorithms). Fort his project, just tested former Machine learning APIs not as prevalent for linked data. What results to compare to?

Test suite 10 queries for each operation (COUNT, SUM, AVG, MIN, MAX) 10 different WHERE CLAUSES Test: Sensitivity calculated from original query Remove each personal URI using “MINUS” keyword and see which removal is most sensitive

Example for Sens Test Query: PREFIX rdf: PREFIX rdfs: PREFIX foaf: PREFIX mimic: SELECT (SUM(?o) as ?aggr) WHERE{ ?s foaf:name ?n. ?s mimic:event ?e. ?e mimic:m1 "Insulin". ?e mimic:v1 ?o. FILTER(isNumeric(?o)) }

Example for Sens Test Sensitivity query: PREFIX rdf: PREFIX rdfs: PREFIX foaf: PREFIX mimic: SELECT (SUM(?o) as ?aggr) WHERE{ ?s foaf:name ?n. ?s mimic:event ?e. ?e mimic:m1 "Insulin". ?e mimic:v1 ?o. FILTER(isNumeric(?o)) MINUS {?s foaf:name "%s"} } % (name)

Results Query 6 - Error

Runtime Queries were also tested for runtime. Bigger WHERE clauses More keywords Extra overhead of doing the calculations.

Results Query 6 - Runtime

Interpretation Sensitivity calculation time on-par with query time Might not be good for big data Find ways to reduce sensitivity calculation time? AVG does not do so well… Approximation yields too much noise vs. trying all possibilities Runs ~4x slower than simple querying Solution 1: Look at all data manually (large data transfer) Solution 2: Can we use NOISY_SUM / NOISY_COUNT instead?

Conclusion

Contributions Theory on how to apply differential privacy to linked data. Experimental implementation of differential privacy. Verification that it is applied correctly. Overall privacy module for SPARQL queries. Limited but a good start Other: Updated sparql to n3 translation to Sparql version 1.1 Expanded upon IARPA project to create policies against statistical queries.

Shortcomings and Future Work Triplestores need some structure for this to work Personal information must be explicitly defined in triples. Is there a way to automatically detect what triples would constitute private information? Complexity Lots of noise for sparse data. Can divide data into disjoint sets to reduce noise like PINQ does Use localized sensitivity measures? Third party software problems Would this work better using a different Triplestore implementation?

Other work Other implementations: PINQ Airavat PDDP Some of the Theoretical Work Out There Differential privacy paper Exponential Mechanism Noise Calculation Differential Privacy and Machine Learning

Appendix: Results Q1, Q2 Q2ErrorQuery_TimeSens_Calc_Time COUNT SUM AVG MAX MIN

Appendix: Results Q3, Q4 Q3ErrorQuery_TimeSens_Calc_Time COUNT SUM AVG MAX MIN Q4ErrorQuery_TimeSens_Calc_Time COUNT SUM AVG MAX MIN

Appendix: Results Q5, Q6 Q5ErrorQuery_TimeSens_Calc_Time COUNT SUM AVG MAX MIN Q6ErrorQuery_TimeSens_Calc_Time COUNT SUM AVG MAX MIN

Appendix: Results Q7, Q8 Q7ErrorQuery_TimeSens_Calc_Time COUNT SUM AVG MAX MIN Q8ErrorQuery_TimeSens_Calc_Time COUNT SUM AVG MAX MIN

Appendix: Results Q9, Q10 Q9ErrorQuery_TimeSens_Calc_Time COUNT SUM AVG MAX MIN Q10ErrorQuery_TimeSens_Calc_Time COUNT SUM AVG MAX MIN