Introduction to Data Mining

Transcription

1 Introduction to Data Mining Privacy preserving data mining Li Xiong Slides credits: Chris Clifton Agrawal and Srikant 4/3/2011 1

2 Privacy Preserving Data Mining Privacy concerns about personal data AOL query log release Netflix challenge Data scraping

3 A race to the bottom: privacy ranking of Internet service companies A study done by Privacy International into the privacy practices of key Internet based companies Amazon, AOL, Apple, BBC, ebay, Facebook, Friendster, Google, LinkedIn, LiveJournal, Microsoft, MySpace, Skype, Wikipedia, LiveSpace, Yahoo!, YouTube

4 A Race to the Bottom: Methodologies Corporate administrative details Data collection and processing Data retention Openness and transparency Customer and user control Privacy enhancing innovations and privacy invasive innovations

5 A race to the bottom: interim results revealed

6 Why Google Retains a large quantity of information about users, often for an unstated or indefinite length of time, without clear limitation on subsequent use or disclosure Maintains records of all search strings with associated IP and time stamps for at least months Additional personal information from user profiles in Orkut Use advanced profiling system for ads

7 Remember, they are always watching

8 Some advice from privacy Use cash when you can. campaigners Do not give your phone number, social-security number or address, unless you absolutely have to. Do not fill in questionnaires or respond to telemarketers. Demand that credit and data-marketing firms produce all information they have on you, correct errors and remove you from marketing lists. Check your medical records often. Block caller ID on your phone, and keep your number unlisted. Never leave your mobile phone on, your movements can be traced. Do not user store credit or discount cards If you must use the Internet, encrypt your , reject all cookies and never give your real name when registering at websites Better still, use somebody else s computer

9 Privacy-Preserving Data Mining Data obfuscation (non-interactive model) Original Data Anonymization Sanitized Data Miner Output perturbation (interactive model) Original Data Access Interface Perturbed Results Miner

10 Classes of Solutions Methods Input obfuscation Perturbation Generalization Output perturbation Metrics Differential privacy Privacy vs. Utility

11 Data randomization Data Perturbation Randomization (additive noise) Geometric perturbation and projection (multiplicative noise) Randomized response technique (categorical data)

12 Randomization Based Decision Tree Learning (Agrawal and Srikant 00) Basic idea: Perturb Data with Value Distortion User provides x i +r instead of x i r is a random value Uniform, uniform distribution between [-α, α] Gaussian, normal distribution with µ = 0, σ Hypothesis Miner doesn t see the real data or can t reconstruct real values Miner can reconstruct enough information to identify patterns

13 Classification using Randomization Data Alice s age 30 70K K Add random number to Age 30 becomes 65 (30+35) Randomizer Randomizer 65 20K K......? Classification Algorithm Model

14 Output: A Decision Tree for buys_computer age? <=30 overcast >40 student? yes credit rating? no yes excellent fair no yes yes February 12, 2008 Data Mining: Concepts and Techniques 14

15 Attribute Selection Measure: Gini index (CART) If a data set D contains examples from n classes, gini index, gini(d) is defined as gini ( D) = 1 n p 2 j j = 1 where p j is the relative frequency of class j in D If a data set D is split on A into two subsets D 1 and D 2, the gini index gini(d) is defined as Reduction in Impurity: D ( ) 1 D ( ) 2 gini A D = gini D1 + gini ( D 2) D D gini( A) = gini( D) gini ( D) The attribute provides the smallest gini split (D) (or the largest reduction in impurity) is chosen to split the node A February 12, 2008 Data Mining: Concepts and Techniques 15

16 Randomization Approach Overview Alice s age 30 70K K Add random number to Age 30 becomes 65 (30+35) Randomizer Randomizer 65 20K K Reconstruct Distribution of Age Reconstruct Distribution of Salary... Classification Algorithm Model

17 Original Distribution Reconstruction x 1, x 2,, x n are the n original data values Drawn from n iid random variables with distribution X Using value distortion, The given values are w 1 = x 1 + y 1, w 2 = x 2 + y 2,, w n = x n + y n y i s are from n iid random variables with distribution Y Reconstruction Problem: Given F Y and w i s, estimate F X

18 Original Distribution Reconstruction: Method Bayes theorem for continuous distribution The estimated density function (minimum mean square error estimator): n 1 f Y ( w i a) f X ( a) f X ( a ) = n i= 1 f w z f zdz Iterative estimation The initial estimate for f X at j=0: uniform distribution Iterative estimation f j X ( a) = n n i= 1 Y ( ) ( ) f Y f Y i Stopping Criterion: difference between successive iterations is small X j ( wi a) fx ( a) j ( w z) f ( z) i X dz

19 Reconstruction of Distribution 1200 People Number of Original Randomized Reconstructed Age

20 Original Distribution Reconstruction

21 Original Distribution Construction for Decision Tree When are the distributions reconstructed? Global Reconstruct for each attribute once at the beginning Build the decision tree using the reconstructed data ByClass First split the training data Reconstruct for each class separately Build the decision tree using the reconstructed data Local First split the training data Reconstruct for each class separately Reconstruct at each node while building the tree

22 Accuracy vs. Randomization Level Fn 3 Accuracy Randomization Level Original Randomized ByClass

23 More Results Global performs worse than ByClass and Local ByClass and Local have accuracy within 5% to 15% (absolute error) of the Original accuracy Overall, all are much better than the Randomized accuracy

24 Privacy metrics Privacy metrics of random additive data perturbation 4/3/2011 Data Mining: Principles and Algorithms 24

25 Unfortunately Random additive data perturbation are subject to data reconstruction attacks Original data can be estimated using spectral filtering techniques H. Kargupta, S. Datta. On the privacy preserving properties of random data perturbation techniques, in ICDM /3/2011 Data Mining: Principles and Algorithms 25

26 Estimating distribution and data values 4/3/2011 Data Mining: Principles and Algorithms 26

27 Follow-up Work Multiplicative randomization Geometric randomization Also subjective to data reconstruction attacks! Known input-output Known samples 4/3/2011 Data Mining: Principles and Algorithms 27

28 Data randomization Data Perturbation Randomization (additive noise) Geometric perturbation and projection (multiplicative noise) Randomized response technique (categorical data)

29 Data Collection Model Data cannot be shared directly because of privacy concern

30 Background: Randomized Response The true answer is Yes Do you smoke? Biased coin: P( Yes) = θ Head Yes P( Head) = θ ( θ 0.5) θ 0.5 Tail No P'(Yes) =P(Yes) θ +P(No) (1 θ) P'(No) =P(Yes) (1 θ) +P(No) θ

31 Decision Tree Mining using Randomized Response Multiple attributes encoded in bits Biased coin: P( Yes) = θ Head True answer E: 110 P ( Head ) = θ θ 0.5 ( θ 0.5) Tail False answer!e: 001 Column distribution can be estimated for learning a decision tree Using Randomized Response Techniques for Privacy-Preserving Data Mining, Du, 2003

32 Generalization for Multi-Valued Categorical Data q1 q2 q3 q4 S i S i+1 S i+2 True Value: S i S i+3 P'(s1) P'(s2) P'(s3) P'(s4) = q1 q4 q3 q2 P(s1) q2 q1 M q4 q3 P(s2) q3 q2 q1 q4 P(s3) q4 q3 q2 q1 P(s4)

33 A Generalization RR Matrices [Warner 65], [R.Agrawal 05], [S. Agrawal 05] RR Matrix can be arbitrary a 11 a 12 a 13 a 14 a M = 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 a 41 a 42 a 43 a 44 Can we find optimal RR matrices? OptRR:Optimizing Randomized Response Schemes for Privacy-Preserving Data Mining, Huang, 2008

34 What is an optimal matrix? Which of the following is better? M 1 = M 2 = Privacy: M 2 is better Utility: M 1 is better So, what is an optimal matrix?

35 Optimal RR Matrix An RR matrix M is optimal if no other RR matrix s privacy and utility are both better than M (i, e, no other matrix dominates M). Privacy Quantification Utility Quantification Privacy and utility metrics Privacy: how accurately one can estimate individual info. Utility: how accurately we can estimate aggregate info.

36 Optimization algorithm Evolutionary Multi-Objective Optimization (EMOO) The algorithm Start with a set of initial RR matrices Repeat the following steps in each iteration Mating: selecting two RR matrices in the pool Crossover: exchanging several columns between the two RR matrices Mutation: change some values in a RR matrix Meet the privacy bound: filtering the resultant matrices Evaluate the fitness value for the new RR matrices. Note : the fitness values is defined in terms of privacy and utility metrics

37 Output of Optimization The optimal set is often plotted in the objective space as Pareto front. Worse M 6 M 5 M 8 M 7 M 4 Utility M 1 M 2 M 3 Privacy Better

38 Classes of Solutions Methods Input obfuscation Perturbation Generalization Output perturbation Differential privacy Metrics Privacy vs. Utility

39 Data Re-identification Disease Birthdate Sex Zip Name

40 k-anonymity & l-diversity 40

41 Privacy preserving data mining Generalization principles k-anonymity, l-diversity, Methods Optimal Greedy Top-down vs. bottom-up 41

42 Mondrian: Greedy Partitioning Algorithm Problem Need an algorithm to find multi-dimensional partitions Optimal k-anonymous strict multi-dimensional partitioning is NP-hard Solution Use a greedy algorithm Based on k-d trees Complexity O(nlogn)

43 Example k = 2; Quasi Identifiers: Age, Zipcode What should be the splitting criteria? Patient Data Multi-Dimensional

44 Unfortunately Generalization based principles and methods are subjective to attacks Background knowledge sensitive Attack dependent 4/3/2011 Data Mining: Principles and Algorithms 44

45 Classes of Solutions Methods Input obfuscation Perturbation Generalization Output perturbation Metrics Differential privacy Privacy vs. Utility

46 Differential Privacy Differential privacy requires the outcome to be formally indistinguishable when run with and without any particular record in the data set D1 Bob in D2 Bob out Differentially Private Interface Q Q(D1) + Y1 User Q(D2) + Y2 A(D1) A(D2)

47 Differential Privacy Differential privacy Laplace mechanism Q(D) + Y where Y is drawn from Query sensitivity D1 Bob in D2 Bob out Differentially Private Interface Q(D1) + Y1 Q Q(D2) + Y2 User A(D1) A(D2)

48 Coming up Data mining algorithms using differential privacy Decision tree learning (Data Mining with Differential Privacy, SIGKDD 10) Frequent itemsets mining (discovering frequent patterns in sensitive data, SIGKDD 10) 4/3/2011 Data Mining: Principles and Algorithms 48

49 Midterm Exam Adjusted mean: 85.3 Adjusted max: 101 Your favorite topics: Clustering, frequent itemsets mining, decision tree Your favorite assignments: Apriori Your least favorite: SOM, Weka analysis 4/3/2011 Data Mining: Principles and Algorithms 49