Background

Knowledge Attack for Generalization based Privacy-Preserving Data Mining

Discussion Outline

(sigmod08-4)Privacy-MaxEnt: Integrating Background Knowledge in Privacy Quantification

(kdd08-4) Composition Attacks and Auxiliary Information in Data Privacy

(vldb07-4) Privacy Skyline: Privacy with Multidimensional Adversarial Knowledge

Anonymization techniques

Generalization & suppression Consistency property: multiple occurrences of the

same value are always generalized the same way. (all old methods and recent Incognito)

No consistency property (Mondrain) Anatomy (Tao vldb06) Permutation (Koudas ICDE07)

Anonymization through Anatomy

Anatomy: simple and effective privacy preservation

Anonymization through permutation

Background knowledge

K-anonymity Attacker has access to public databases, i.e., quasi-

identifier values of the individuals. The target individual is in the released database.

L-diversity Homogeneity attack background knowledge about some individuals’ sensitive

attribute values T-closeness

The distribution of sensitive attribute in the overall table

Type of background knowledge Known facts

A male patient cannot have ovarian cancer Demographical information

It is unlikely that a young patient of certain ethnic groups has heart disease

Some combination of the quasi-identifier values cannot entail some sensitive attribute values

Type of background knowledge Adversary-specific knowledge

target individual has no specific sensitive attribute value , e.g., Bob does not have flu

Sensitive attribute values of some other individuals, Joe, John, and Mike (as Bob’s neighbor) have flu

Knowledge about same-value family

Some extension

Multiple sensitive values per individual Flu \in Bob[S] Basic implication (adopted in Martin ICDE07)

cannot practically express the above --- |s|-1 basic implications are needed

Probabilistic knowledge vs. deterministic knowledge

Data SetsIdentifier Quasi-Identifier (QI) Sensitive Attribute (SA)

how much adversaries can know about an individual’s sensitive attributes if they know the individual’s quasi-identifiers

we need to measure P(SA|QI)

Quasi-Identifier (QI) Sensitive Attribute (SA)

Background Background KnowledgeKnowledge

Impact of Background Knowledge

Background Knowledge:

It’s rare for male to have breast cancer.

[Martin, et al. ICDE’07]

first formal study of the effect of background knowledge on privacy-

preserving

Assumption the attacker has complete information about individuals’ non-sensitive data

Full identification information

Name Age Sex Zipcode Disease

Andy 4 M 12000 gastric ulcer

Bill 5 M 14000 dyspepsia

Ken 6 M 18000 pneumonia

Nash 9 M 19000 bronchitisAlice 12 F 22000 flu

Full identification information

Rule based knowledge

Atom Ai a predicate about a person and his/her sensitive

values tJack[Disease] = flu

says that the Jack’s tuple has the value flu for the sensitive attribute Disease.

Basic implication

Background knowledge formulated as conjunctions of k basic implications

The idea

use k to bound the background knowledge, and compute the maximum disclosure of a bucket data set with respect to the background knowledge.

(vldb07-4)

[Bee-Chung, et al. VLDB’07]

use a triple (l, k,m) to specify the bound ofthe background rather than a single k

Introduction

[Martin, et al. ICDE’07] limitation of using a single number k to bound background knowledge

quantifying an adversary’s external knowledge by a novel multidimensional novel multidimensional approachapproach

Problem formulation

Pr(Pr(t t has has s s | | KK, , DD*)*)

data owner has a table of data (denoted by D)data owner publishes the resulting release candidate D*

S: a sensitive attributes: a target sensitive valuet: a target individual

new bound specifies that adversaries know l other people’s sensitive value; adversaries know k sensitive values that the

target does not have adversaries know a group of m−1 people who

share the same sensitive value with the target

Theoretical framework

(sigmod08-4)

[Wenliang, et al. SIGMOD’08]

Introduction

The impact of background knowledge: How does it affect privacy? How to measure its impact on privacy?

Integrate background knowledge in privacy quantification. Privacy-MaxEnt: A systematic approach. Based on well-established theories.

maximum entropy estimate

Challenges

Directly computing P( S | Q ) is hard.

What do we want to compute? P( S | Q ), given the background knowledge and

the published data set.

Our Approach

BackgroundKnowledge

Published Data

Public Information

Constraintson x

Constraintson x

Solve x

Consider P( S | Q ) as variable x (a vector).

Most unbiased solution

Maximum Entropy Principle

“Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum entropy estimate. It is least biased estimate possible on the given information.” — by E. T. Jaynes, 1957.

The MaxEnt Approach

BackgroundKnowledge

Published Data

Public Information

Constraintson P( S | Q )

Constraintson P( S | Q )

Estimate P( S | Q )

Maximum Entropy Estimate

Entropy

Because H(S | Q, B) = H(Q, S, B) – H(Q, B)

Constraint should use P(Q, S, B) as variables

BSQ

BQSPBQSPBQPBQSH,,

).,|(log),|(),(),|( :Entropy

BSQ

BSQPBSQPBSQH,,

).,,(log),,(),,( :Entropy

Maximum Entropy Estimate

Let vector x = P(Q, S, B). Find the value for x that maximizes its

entropy H(Q, S, B), while satisfying h1(x) = c1, …, hu(x) = cu : equality constraints

g1(x) ≤ d1, …, gv(x) ≤ dv : inequality constraints

A special case of Non-Linear Programming.

Putting Them Together

BackgroundKnowledge

Published Data

Public Information

Constraintson P( S | Q )

Constraintson P( S | Q )

Estimate P( S | Q )

Maximum Entropy Estimate

Tools: LBFGS, TOMLAB, KNITRO, etc.

Conclusion

Privacy-MaxEnt is a systematic method Model various types of knowledge Model the information from the published data Based on well-established theory.

(kdd08-2)

[Srivatsava, et al. KDD’08]

Introduction

reason about privacy in the face of rich, realistic sources of auxiliary information.

investigate the effectiveness of current anonymization schemes in preserving privacy when multiple organizations independently release anonymized data

present a composition attacks an adversary uses independently anonymized

releases to breach privacy

Summary What is background knowledge?

Probability-Based Knowledge P (s | q) = 1. P (s | q) = 0. P (s | q) = 0.2. P (s | Alice) = 0.2. 0.3 ≤ P (s | q) ≤ 0.5. P (s | q1) + P (s | q2) = 0.7

Logic-Based Knowledge (proposition/ first order/ modal logic) One of Alice and Bob has “Lung Cancer”.

Numerical data 50K ≤ salary of Alice ≤ 100K age of Bob ≤ age of Alice

Linked data degree of a node topology information ….

Domain Knowledge mechanism or algorithm of anonymization

for data publication independently released anonymized data by other organizations

And many many others ….

Summary How to represent background knowledge?

Probability-Based Knowledge P (s | q) = 1. P (s | q) = 0. P (s | q) = 0.2. P (s | Alice) = 0.2. 0.3 ≤ P (s | q) ≤ 0.5. P (s | q1) + P (s | q2) = 0.7

Logic-Based Knowledge (proposition/ first order/ modal logic) One of Alice and Bob has “Lung Cancer”.

Numerical data 50K ≤ salary of Alice ≤ 100K age of Bob ≤ age of Alice

Linked data degree of a node topology information ….

Domain Knowledge mechanism or algorithm of anonymization

for data publication independently released anonymized data by other organizations

And many many others ….

[Martin, et al. ICDE’07]Rule-based

[Wenliang, et al. SIGMOD’08]

[Srivatsava, et al. KDD’08]

[Raymond, et al. VLDB’07]

general knowledge framework

too hard to give a unified framework and give a general solution

Summary

How to quantify background knowledge? by the number of basic implications(association rules)

by a novel multidimensional approach formulated as linear constraints

How one can reason about privacy in the presence of external knowledge? quantify the privacy quantify the degree of randomization required quantify the precise effect of background knowledge

[Charu ICDE’07]

[Martin, et al. ICDE’07]

[Wenliang, et al. SIGMOD’08]

[Bee-Chung, et al. VLDB’07]

[Martin, et al. ICDE’07]

[Wenliang, et al. SIGMOD’08]

Questions? Thanks to Zhiwei Li