Data mining with differential privacy @ KDD'10

1. +
Data Mining with Differential Privacy
Arik Friedman and Assaf Schuster / KDD’10
Chang Wei-Yuan
2014 / 10 / 3 (Fri.) @ MakeLab Group Meeting

2. +Outline
n Introduction
n Background
n Method
n Experiment
n Conclusion
n Though
2

3. +Introduction
n There is great value in data mining
solutions.
n reliable privacy guarantees
n available accuracy
n Differential privacy
n computations are insensitive to changes in
any particular individual's record
3

4. +Introduction (cont.)
n Once an individual is certain that his or
her data will remain private, being opted
in or out of the database should make
little difference.
4

5. +
Introduction (cont.)
n Example1
Name
Result
Tom
0
Jack
1
Henry
1
Diego
0
Alice
?
5
n f(i) = count(i)
n Alice = i=5
n count(5) – count(4)

6. +
Introduction (cont.)
n Example2
n We can speculate the target based on
the information.
6
Id
Sex
Job
Hometown
Hobby
1
M
student
Hsinchu
sport
2
M
teacher
Taipei
writing
3
F
student
Hsinchu
Singing
4
F
student
Taipei
Singing
5
?
?
?
?

7. +Introduction (cont.)
n Goal：count(5) – count(4) ≈ 0
n Goal：” computations are insensitive to
changes in any particular individual's
record ”
7

8. +Outline
n Introduction
n Background
n Method
n Experiment
n Conclusion
n Though
8

9. +Differential Privacy
n Differential privacy
9
Output
Probability
• M：a randomized computation
• f：a query function
• D, D’：the datasets with
symmetric difference

10. +Differential Privacy (cont.)
n Differential privacy
10
Define.（ε-Differential Privacy）
We say a randomized computation M provides
differential privacy if for any datasets A and B with
symmetric difference AΔB=1, and set of possible
outcomes S ⊆ Range(M)

11. +Laplace Mechanism
n Example of Laplace Mechanism
11
Name
Result
Tom
0
Jack
1
Henry
1
Diego
0
Alice
?
n count(4) = 2 + noise(4)
n count(5) = 3 + noise(5)
n count(5) – count(4) = eε

12. +Laplace Mechanism
n Laplace Mechanism
12
Theorem. （Laplace mechanism）
Given a function f over an arbitrary domain D, the
computation
provides differential privacy.

13. +Exponential Mechanism
n Example of Exponential Mechanism
13
item
q
ε=0
ε=0.1
ε=1
Football 30
0.46
0.42
0.92
Volleyball
25
0.38
0.33
0.07
Basketball
8
0.12
0.14
1.5E-05
Tennis
2
0.03
0.10
7.7E-07

14. +Exponential Mechanism (cont.)
n Exponential Mechanism
14
Theorem. （Exponential Mechanism）
Let q be a quality function, given a database d,
assigns a score r to each outcome. Then the
mechanism M, defined by
maintains differential privacy.

15. +PINQ Framework
n PINQ Framework
n PINQ is a proposed architecture for data
analysis with differential privacy
n Another operator presented in PINQ is
partition which was dubbed parallel
composition.
n the costs do not add up when queries are executed
on disjoint datasets
15

16. +PINQ Framework (cont.)
16

17. +Outline
n Introduction
n Background
n Method
n Experiment
n Conclusion
n Though
17

18. +Method
18
n SQL-based ID3
n DiffP-ID3
n DiffP-C4.5

19. +SuL-based ID3
n Based on SuLQ framework and Using
Laplace Mechanism.
n It makes direct use of the NoisyCount
primitive to evaluate the information gain
criterion.
n It required to evaluate the information
gain should be carried out for each
attribute separately.
n the budget per query is small
19

20. +SuL-based ID3
n ID3 Classification
n Split point
n max( Gain(Job), Gain(Home), Gain(Hobby) )
20
Id
Sex
Job
Hometown
Hobby
1
M
student
Hsinchu
sport
2
M
teacher
Taipei
writing
3
F
student
Hsinchu
Singing
4
F
student
Taipei
Singing

21. +SuL-based ID3
n SuL-based ID3 Classification
n Split point
n max( Gain(Job)+Noisy, Gain(Home)+Noisy,
Gain(Hobby)+Noisy )
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Id
Sex
Job
Hometown
Hobby
1
M
student
Hsinchu
sport
2
M
teacher
Taipei
writing
3
F
student
Hsinchu
Singing
4
F
student
Taipei
Singing

22. +DiffP-ID3
n Based on PINQ framework and using
exponential mechanism.
n It evaluates all attributes simultaneously
in one query, the outcome of which is
the attribute to use for splitting.
n the quality function q provided to the scores
each attribute
22

23. +DiffP-ID3 (cont.)
n DiffP-ID3 Classification
n Split point
n Max( Gain(M(Job)), Gain(M(Job)),
Gain(M(Hobby)) )
n PINQ Partition
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Id
Sex
Job
Hometown
Hobby
1
M
student
Hsinchu
sport
2
M
teacher
Taipei
writing
3
F
student
Hsinchu
Singing
4
F
student
Taipei
Singing

24. +DiffP-ID3 (cont.)
n Which quality function should be fed into
the exponential mechanism?
n the depth constraint
n the sensitivity of the splitting criterion
n Information gain will be the most
sensitive to noise, and Max operator will
be the least sensitive to noise.
24

25. +DiffP-C4.5
n One important extension is the ability to
handle continuous attributes.
n First, the domain is divided into ranges where
the score is constant. Each range is
considered a discrete option.
n Then, a point from the range is sampled with
uniform distribution and returned as the output
of the exponential mechanism.
25

26. +Outline
n Introduction
n Background
n Method
n Experiment
n Conclusion
n Though
26

27. +Experiment
n It define a domain with ten nominal
attributes and a class attribute from
another paper.
n It introduces noise to the samples by
reassigning attributes and classes,
replacing each value with probability
noise.
n For testing, it generated similarly a
noiseless test set with 10, 000 records.
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28. + 28
n the average accuracy is higher as more training
samples are available
n the influence of the noise weakens as the
number of samples grows using Gini and Max

29. + 29
n three of the ten attributes were replaced with
numeric attributes over the domain [0, 100]
n Figure 4 presents the results of a similar
experiment

30. + 30
n for smaller training sets, ID3 allows for better
accuracy
n for larger training sets, C4.5 is better than ID3

31. + 31
n the accuracy results presented in Figure 6 was
around 5% and even lower than the results
presented in Figure 7
n when the sizeof the dataset is small, algorithms
that make efficient use of the privacy budget are
superior

32. +Outline
n Introduction
n Background
n Method
n Experiment
n Conclusion
n Though
32

33. +Conclusion
n When the number of training samples is
relatively small or the privacy constraints
set by the data provider are very limiting,
the sensitivity of the calculations
becomes crucial.
33

34. +Future work
n One solution might be to consider other
stopping rules when selecting nodes,
trading possible improvements in
accuracy for increased stability.
n In addition, it may be fruitful to consider
different tactics for budget distribution.
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35. +Outline
n Introduction
n Background
n Method
n Experiment
n Conclusion
n Though
35

36. +
Thought
36

37. +
Thanks for listening.
2014 / 10 / 3 (Fri.) @ MakeLab Group Meeting
v123582@gmail.com