Cardinality-based Inference Control in OLAP Systems An Information Theoretic Approach

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Cardinality-based Inference Control in OLAP
SystemsAn Information Theoretic Approach

• Nan Zhang
• Texas AM University
• This is a joint work with Dr. Wei Zhao and Dr.
  Jianer Chen

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Privacy Concern

• Growing Privacy Concern in Database Applications
  on the Internet (e.g., Data Mining)
• 17 privacy fundamentalists, 56 pragmatic
  majority, 27 marginally concerned (ATT Survey)
• Challenge Can we build accurate models of the
  aggregate data without access to the precise
  values of individual data?

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Problem Definition

• Will the application invade privacy?

Application (Data Miner)
OLAP Server
Randomization
Data Providers
DataProviders

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Inference Problem
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Inference Problem

• SU 20
• S1S3-SB-ST 87

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Goal

• Reject queries that may result in an inference
  problem
• Answer as many other queries as we can

Application (Data Miner)
OLAP Server
Database
DataWarehouse
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Related Work

• A lot of work on statistical databases
• Survey
• Differences
• Restriction on OLAP queries
• Structure of data cube
• Online response time

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Related Work

• A similar scheme
• Our Advantages
• Much easier approach
• A tighter bound
• More general framework

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Definition Query
1-dimensional queries
2-dimensional queries
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Data Cube and Lattice of Cuboids
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Definition Query

• There exists a unique cuboid S such that a cell
  of S is the aggregation of W.
• Suppose that S is a k-dimensional cuboid. The
  dimensionality of Q is defined to be n - k.

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Definition compromisability
SU Sales amount of used books in Feb
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Definition compromisability

• Compromisability
• direct inference
• Compromisability lt 1

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Cardinality-based Inference Control
S3, ST Minimum compromisability 2,
21(43)-222-1 5 gt 2
S1, SB Minimum compromisability 2,
21(43)-222-1 5 5
S1, SD Minimum compromisability 2,
21(43)-222-1 5 gt 4
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Our Approach

• A k-dimensional query Q(F, W) can be safely
  answered if every k1 dimensional dice X in X
  that
• Contains W as a subset
• Can be queries as a cell of a (n-k-1)-dimensional
  cuboid
• satisfies

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Comparison with Previous Result

• vs.

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Proof of Our Bound

• Basic idea

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An Information-Theoretic Definition

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An Information-Theoretic Definition

• Let
• we have
• Thus, no inference problem exists in a data cube
  X if

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Bounds on fmax(t0)
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Maximum Non-Compromisable Data Cube
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Main Theorem

• Let
• we have

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Final Remarks

• Future Work
• Quantitative measure of the inference problem
• Combination of randomization and inference
  control approaches

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Thank you

• Questions