1. Privacy-Preserving Data Mining
Representor : Li Cao
October 15, 2003

2. Presentation organization
Associate Data Mining with Privacy
Privacy Preserving Data Mining scheme using random perturbation
Privacy Preserving Data Mining using Randomized Response Techniques
Comparing these two cases

3. Privacy protection history Privacy concerns nowadays
Citizens’ attitude
Scholars’ attitude

4. Internet users’ attitudes

5. Privacy value Filtering to weed out unwanted information
Better search results with less effort
Useful recommendations
Market trend …………
Example:
From the analysis of a large number of purchase transaction records with the costumers’ age and income, we know what kind of costumers like some style or brand.

6. Motivation (Introducing Data Mining )
Data Mining’s goal: discover knowledge, trends, patterns from large amounts of data.
Data Mining’s primary task: developing accurate models about aggregated data without access to precise information in individual data records. (Not only discovering knowledge but also preserving privacy)

7. Presentation organization
Associate Data Mining with Privacy
Privacy Preserving Data Mining scheme using random perturbation
Privacy Preserving Data Mining using Randomized Response Techniques
Comparing these two cases

8. Privacy Preserving Data Mining scheme using random perturbation
Basic idea
Reconstruction procedure
Decision-Tree classification
Three different algorithms

9. Attribute list of a example

10. Records of a example

11. Privacy preserving methods
Value-class Membership: the values for an attribute are partitioned into a set of disjoint, mutually-exclusive classes.
Value Distortion: xi+r instead of xi where r is a random value.
a) Uniform
b) Gaussian

12. Basic idea
Original data  Perturbed data (Let users provide a modified value for sensitive attributes)
Estimate the distribution of original data from perturbed data
Build classifiers by using these reconstructed distributions (Decision-tree)

13. Basic Steps

14. Reconstruction problem
View the n original data value x1,x2,…xn of a one-dimensional distribution as realizations of n independent identically distributed (iid) random variables X1,X2,…Xn, each with the same distribution as the random variable X.
To hide these data values, n independent random variables Y1,Y2…Yn have been used, each with the same distribution as a different random variable Y.

15. Given x1+y1, x2+y2…xn+yn (where yi is the realization of Yi) and the cumulative distribution function Fy for Y, we would like to estimate the cumulative distribution function Fx for X.
In short, given a cumulative distribution Fy and the realizations of n iid random samples X1+Y1, X2+Y2,…Xn+Yn, estimate Fx.

16. Reconstruction process
Let the value of Xi+Yi be wi (xi+yi). Use Bayes’ rule to estimate the posterior distribution function Fx1’ (given that X1+Y1=w1) for X1, assuming we know the density function fx and fy for X and Y respectively.

17. To estimate the posterior distribution function Fx’ given x1+y1, x2+y2…xn+yn, we average the distribution function for each of the Xi.

18. The corresponding posterior density function, fx’ is obtained by differentiating Fx’:
Given a sufficiently large number of samples, fx’ will be very close to the real density function fx.

19. Reconstruction algorithm
fx0 := Uniform distribution
j :=0 //Iteration number
Repeat
j := j+1
until (stopping criterion met)

20. Stopping Criterion
Observed randomized distribution ?= The result of randomizing the current estimate of the original distribution
The difference between successive estimates of the original distribution is very small.

21. Reconstruction effect

23. Decision-Tree Classification
Tow stages:
(1) Growth (2) Prune
Example:

24. Tree-growth phase algorithm
Partition (Data S)
begin
if (most points in S are of the same class)
then return;
for each attribute A do
evaluate splits on attribute A;
Use best split to partition S into S1 and S2;
Partition (S1)
Partition (S2)
end

25. Choose the best split Information gain (categorical attributes)
Gini index (continuous attributes)

26. Gini index calculation
(pj is the relative frequency of class j in S)
If a split divides S into two subsets S1 and S2
Note: Calculating this index requires only the distribution of the class values.

28. When & How original distribution are reconstructed
Global: Reconstruct the distribution for each attribute once. Decision-tree classification.
ByClass: For each attribute, first split the training data by class, then reconstruct the distributions separately. Decision-tree classification
Local: The same as in ByClass, however, instead of doing reconstruction only once, reconstruction is done at each node.

29. Example (ByClass and Local)

30. Comparing the three algorithms
Execution Time
Accuracy
Global
Cheapest
Worst
ByClass
Middle
Local
Most expensive
Best

31. Presentation Organization
Associate Data Mining with Privacy
Privacy Preserving Data Mining scheme using random perturbation
Privacy Preserving Data Mining using Randomized Response Techniques
Comparing these two cases
Are there any other classification methods available?

32. Privacy Preserving Data Mining using Randomized Response Techniques
Building Decision-Tree
Key: Information Gain Calculation
Experimental results

33. Randomized Response A survey contains a sensitive attribute A.
Instead of asking whether the respondent has the attribute A, ask two related questions, the answer to which are opposite to each other (have A  no A).
Respondent use a randomizing device to decide which question to answer. The device is designed in such way that the probability of choosing the first question is θ .

34. To estimate the percentage of people who has the attribute A, we can use:
P’(A=yes) = P(A=yes)* θ +P(A=no)*(1- θ)
P’(A=no) = P(A=no)* θ +P(A=yes)*(1- θ)
P’(k=yes): The proportion of the “yes” responses obtained from the survey data.
P(k=yes): The estimated proportion of the “yes” responses
Our Goal: P(A=yes) and P(A=no)

35. Example: Sensitive attribute: Married? Two questions: A? Yes / No
B? No / Yes

36. Decision-Tree (Key: Info Gain)
m: m classes assumed
Qj: The relative frequency of class j in S
v: any possible value of attribute A
Sv: The subset of S for which attribute A has value v.
| Sv |: The number of elements in Sv
|S|: The number of elements in S

37. P(E): The proportion of the records in the undisguised data set that satisfy E=true
P*(E): The proportion of the records in the disguised data set that satisfy E=true
Assume the class label is binary.
So the Entropy(S) can be calculated. Similarly, calculate |Sv|. At last, we get Gain(S,A).

38. Experimental results

39. Comparing these two cases
Perturbation
Response
Attribute
Continuous
Categorical
Privacy Preserving method
Value distortion
Randomized response
Choose attribute to split
Gini index
Information Gain
Inverse procedure
Reconstruct distribution
Estimate P(E) from P’(E)

40. Future work Solve categorical problems by the first scheme
Solve continuous problems by the second scheme
Combine these two scheme to solve some problems
Other classification suitable