To Do or Not To Do: The Dilemma of Disclosing

Anonymized Data

Lakshmanan L, Ng R, Ramesh GUniv. of British Columbia

Oren Fine

Nov. 2008

CS Seminar in Databases (236826)

Once Upon a Time…

• The police is after Edgar, a drug lord suspect.– Intel. has gathered calls & meetings data records as a

transactional database– In order to positively frame Edgar, the police must find

hard evidence, and wishes to outsource data mining tasks to “We Mind your Data Ltd.”

– But, the police is subject to the law, and is obligated to keep the privacy of the people in the database – including Edgar, which is innocent until proven otherwise.

– Furthermore, Edgar is seeking for the smallest hint to disappear…

I have the pleasure to introduce Edgar vs. The Police

VS.

Motivation

• The Classic Dilemma:– Keep your data close to your chest and never risk

privacy or confidentiality or…– Disclose the data and gain potential valuable

knowledge and benefits

• In order to decide, we need to answer a major question– “Just how safe is the anonymized data?”– Safe = protecting the identities of the of the objects.

Agenda

• Anonymization

• Model the Attacker’s Knowledge

• Determine the risk to our data

Anonymization or De-Identification

• Transform sensitive data into generated unique content (strings, numbers)

• Example

TIDNames

1{Hussein, Hassan, Dimitri}

2{Hussein, Edgar, Anglea}

3{Angela, Edgar}

4{Raz, Adi, Yishai}

5{Hassan, Yishai, Dimitri, Raz}

6{Raz, Anglea, Nithai}

TIDTransaction

1{1,2,3}

2{1,4,5}

3{5,4}

4{6,7,8}

5{2,8,3,6}

6{6, 5, 9}

Anonymization or De-Identification

• Advantages– Very simple– Does not affect final outcome or perturb data

characteristics

• We do not suggest that anonymization is the “right” way, but it is probably the most common

Frequent Set Mining Crash Course• Transactional database • Each transaction has TID and a set of

items• An association rule of the form XY has

– Support s if s% of the transactions include (X,Y)

– Confidence c if c% of the transactions that include X also include Y

• Support = frequent sets• Confidence = association rules• A k-itemset is a set of k items

Example

TIDNames

1Angela, Ariel, Edgar, Steve, Benny

2Edgar, Hassan, Steve, Tommy

3Joe, Sara, Israel

4Steve, Angela, Edgar

5Benny, Mahhmud, Tommy

6Angela, Sara, Edgar

7Hassan, Angela, Joe, Edgar, Noa

8Edgar, Benny, Steve, Tommy

Example (Cont.)• First, we look for frequent sets, according to a

support threshold• 2-itemsets: {Angela, Edgar}, {Edgar, Steve} have

50% support (4 out of 8 transactions).• 3-itemsets: {Angela, Edgar, Steve}, {Benny,

Edgar, Steve} and {Tommy, Edgar, Steve} have only 25% support (2 out of 8 transactions)

• The rule {Edgar, Steve} {Angela} has 50% confidence (2 out 4 transactions) and the rule {Tommy} {Edgar, Steve} has 66.6% confidence.

Frequent Set Mining Crash Course (You’re Qualified!)

• Widely used in market basket analysis, intrusion detection, Web usage mining and bioinformatics

• Aimed at discovering non trivial or not necessarily intuitive relation between items/variables of large databases“Extracting wisdom out of data”

• Who knows what is the most famous frequent set?

Big Mart’s Database

Modeling the Attacker’s Knowledge

• We believe that the attacker has prior knowledge about the items in the original domain

• The prior information regards the frequencies of items in the original domain

• We capture the attacker’s knowledge with “Belief Functions”

Examples of Belief Functions

Consistent Mapping

• Mapping anonymized entities to original entities only according to the belief function

Ignorant Belief Function (Q)

• How does the graph look like?

• What is the expected number of cracks?

• Suppose n items. Further suppose that we are only interested in a partial group, of size n1

• What is the expected number of cracks now?

• Don’t you underestimate Edgar…

Ignorant Belief Function (A)

Compliant Point-Valued Belief Function (Q)

• How does the graph look like?• What is the expected number of cracks?• Suppose n items. Further suppose that we

are only interested in a partial group, of size n1

• What is the expected number of cracks now?

• Unless he has inner source, we shouldn’t overestimate Edgar either…

Compliant Point-Valued Belief Function (A)

Compliant IntervalBelief Functions

• Direct Computation Method– Build a graph G and adjacency matrix AG

– The probability of cracking k out of n items:

• Computing the permanent is know to be #P-complete problem, state of the art approximation running time O(n22) !!

• What the !#$!% is a permanent or #P-complete?

Permanent

• A permanent of an n*n matrix is

• The sum is over all permutations of 1,2,…• Calculating the permanent is #P-complete• Which brings us to…

nS

n

iiiaAperm

1)(,)(

#P-Complete

• Unlike well known complexity classes which are of decision problems, this is a class of function problems

• "compute f(x)," where f is the number of accepting paths of an NP machine

• Example– NP: Are there any subsets of a list of integers that add

up to zero? – #P: How many subsets of a list of integers add up to

zero?

Chain Belief Functions

Chain Belief Functions

Unfortunately…

• General Belief Function does not always produce a chain…

• We seek for way to estimate the number of cracks.

The O-estimate Heuristic

• Suppose Graph G, interval belief function β.• For each x, let Ox denote the outdegree of x

in G.• The probability of cracking x is simply

• The expected number of cracks is

xO1

Properties of O-estimate• Inexact (hence “estimate”)

• Monotonic

-Compliant Belief Function

• Suppose we “somehow” know which items are guessed wrong

• We sum the O-estimates only over the compliant frequency groups

Risk Assessment

• Worst case \ Best case – unrealistic

• Determine the intervals width– Twice the median gap of all successive

frequency groups– Why?

• Determine the degree of compliancy– Perform binary search on , subject to a

“degree of tolerance” – .

End to End Example

• These Intel. Calls & Meeting DR are classified “Top Secret”

TIDNames1Angela, Ariel, Edgar, Steve, Benny

2Edgar, Hassan, Steve, Tommy

3Joe, Sara, Israel

4Steve, Angela, Edgar

5Benny, Mahhmud, Tommy

6Angela, Sara, Edgar

7Hassan, Angela, Joe, Edgar, Noa

8Edgar, Benny, Steve, Tommy

We Anonymize the Database

IJfreq

Angela14/8

Ariel21/8

Edgar36/8

Steve44/8

Benny53/8

Hassan62/8

Tommy73/8

Joe82/8

Sara92/8

Israel101/8

Noa111/8

Mahhmud121/8

TIDItems

11, 2, 3, 4, 5

23, 6, 4, 7

38, 9, 10

44, 1, 3

55, 7, 12

61, 9, 3

76, 1, 8, 3, 11

83, 5, 4, 7

Frequency Groups

• The gaps between the frequency groups:1/8, 1/8, 1/8, 1/8, 2/8

• The median gap = 1/8

FrequencyItems

1/82, 10, 11, 12

2/86, 8, 9

3/85, 7

4/81, 4

6/83

The Attacker’s Prior KnowledgeIFrequency Group

Angela3/8 – 5/8

Ariel0 – 2/8

Edgar5/8 – 7/8

Steve3/8 – 5/8

Benny2/8 – 4/8

Hassan1/8 – 3/8

Tommy2/8 – 4/8

Joe1/8 – 3/8

Sara1/8 – 3/8

Israel0 – 2/8

Noa0 – 2/8

Mahhmud0 – 2/8

The Graph, By the Way…1

2

4

3

8

5

6

7

10

9

11

12

Angela

Ariel

Edgar

Steve

Benny

Hassan

Tommy

Joe

Sara

Israel

Noa

Mahhmud

Calculating the Risk

• Oest=1/4+1/7+1/3+1/4+1/7+1/9+1/7+ 1/9+1/9+1/7+1/7+1/7 = 2.023

• Now, it’s a question of how much would you tolerate...

• Note, that this is the expected number of cracks. However, if we are interested in Edgar, as we’ve seen in previous lemmas, the probability of crack – 1/3.

Experiments

Open Problems

• The attacker’s prior knowledge remains a largely unsolved issue

• This article does not really deal with frequent sets but rather frequent items– Frequent sets can add more information and

differentiate objects from one frequency group

Modeling the Attacker’s Knowledge in the Real World

• In a report for the Canadian Privacy Commissioner appears a broad mapping of adversary knowledge– Mapping phone directories– CV’s – Inferring gender, year of birth and postal code

from different details– Data remnants on 2nd hand hard disks– Etc.

סוף טוב, הכל טוב

Bibliography

• Lakshmanan L., Ng R., Ramesh G. To Do or Not To Do: The Dilemma of Disclosing Anonymized Data. ACM SIGMOD Conference, 2005.

• Agrawal, R. and Srikant, R. 1994. Fast algorithms for mining association rules. In Proc. 1994 Int. Conf. Very Large Data Bases (VLDB’94), Santiago, Chile, pp. 487–499.

• Pan-Canadian De-Identification Guidelines for Personal Health Information, Khaled El-Emam et al., April 2007.

• Wikipedia– Association rule

– #P

– Permanent

Questions ?