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Data Used in "A BAYESIAN APPROACH TO DATA DISCLOSURE: OPTIMAL
INTRUDER BEHAVIOR FOR CONTINUOUS DATA"
by Stephen E. Fienberg, Udi E. Makov, and Ashish P. Sanil
Background:
==========
In this paper we develop an approach to data disclosure in survey settings by
adopting a probabilistic definition of disclosure due to Dalenius. Our approach
is based on the principle that a data collection agency must consider
disclosure from the perspective of an intruder in order to efficiently evaluate
data disclosure limitation procedures. The probabilistic definition and our
attempt to study optimal intruder behavior lead naturally to a Bayesian
formulation. We apply the methods in a small-scale simulation study using data
adapted from an actual survey conducted by the Institute for Social Research at
York University. (See Sections 1-3 of the paper for details oF the model
formulation and related issues.)
The Data:
========
Our case study uses data from the survey data Elite Canadian
Decision-Makers collected by the Institute for Social Research at York
University. This survey was conducted in 1981 using telephone
interviews and there were 1348 respondents, but many of these did not
supply complete data. We have extracted data on 12 variables, each of which
was measured on a 5-point scale:
Civil-liberties:
- ---------------
C1 - Free speech is just not worth it.
C2 - We have gone too far in pushing equal rights in this country.
C3 - It is better to live in an orderly society than to allow people so
much freedom.
C5 - Free speech ought to be allowed for all political groups.
Attitudes towards Jews:
- ----------------------
A15 - Most Jews don't care what happens to people who are not Jews.
A18 - Jews are more willing than others to use shady practices to
get ahead.
Canada-US relationship:
- ----------------------
CUS1 - Ensure independent Canada.
CUS5 - Canada should have free trade with the USA.
CUS6 - Canada's way of life is influenced strongly by USA.
CUS7 - Canada benefits from US investments.
In addition, we have data on two approximately continuous variables:
Personal information:
- --------------------
Income - Total family income before taxes (with top-coding at \$80,000).
Age - Based on year of birth.
We transformed the original survey data as follows in order to create
a database of approximately continuous variables:
[A] We add categorical variables (all but income) to increase the number
of levels. (When necessary we reversed the order of levels of a response to a
question.) The new variables are defined as follows:
Civil = C1 + C2 + C3 + (8 - C5)
Attitude = A15 + A18
Can/US = (5 - CUS1) + CUS5 + (5 - CUS6) + CUS7
After we removed cases with missing observations and two cases involving
young children, we had a data-base consisting of 662 observations.
[B] In order to enhance continuity, we took the following measures:
Age: We added normal distributed variates, with 0 mean and
variance 4 to all observations.
Income: We added uniform variates on the range of $0 - $10,000 to all incomes
below $80,000. Since all cases of incomes exceeding $80,000 were
lumped together in the survey, we simulated their values by means
of a t(8) distribution. Drawing values from the upper 38% tail of t(8),
we evaluated the values of income as $60,000 + 25,000*t(8).
Other variables: We added normal distributed variates, with 0 mean and
variance 0.5 to the variables.
We assume that the agency releases information about all
variables, except for Attitudes (towards Jews), which is unavailable to
the intruder and is at the center of the intruder's investigation.
We denote the released data by
Z = (( z(i,j) )) with i=1,..,662; j=1,2,3,4.
We assume that the intruder's data, X, are accurate and are related to Z via
the following transformation:
x(0,j) = z(i,j)*theta(i,j) + xi(j),
where theta(i,j) is a bias removing parameter normally distributed with mean 1
and variance v(j), and xi(j) is normally distributed disturbance with 0 mean
and variance sigma2(j).
The following table provides the values of
v(j), sigma2(j) used in the study:
v(j) sigma2(j)
Civil 0.1732 25
Can/US 0.1732 25
Age 0.1732 9
Income (in $10000's) 0.1732 4
We first generated several realizations of the above transformation on small
subsets of the data to ascertain the impact of the process of the error
on the data. In Table 4-1 in the paper we present 10 records the the intruder's
accurate data, X, and the biased and corrupted released data, Z, which we
obtained from one realization of the transformation.
Section 4.2 of the paper contains details of the implementation of our Bayesian
model.
Data Used in the Computations:
=============================
We conducted a complete simulation of the procedures for the complete set of
662 cases. We considered four different scenarios for the simulation. (The
names of datasets used in each of the scenarios appear in brackets below. The
datasets are appended to this text.)
* The released data contains no bias or noise (i.e. v(j)=0 and sigma2(j)=0 for
all j). [Z.DATA]
* The released data contains only noise (i.e., v(j)=0 for all j and
and $sigma2(j)$ as given in the above Table). [X_NOISE.DATA]
* The released data contains only bias (i.e., sigma2(j)=0 for all j and v(j)
as given in the above Table). [X_BIAS.DATA]
* The released data contains both bias and noise (i.e., v(j) and sigma2(j) as
given in the above Table). [X_TAMPERED.DATA]
We took each individual in turn as the object of the intruder's efforts and
carried out the calculations.
Structure of the Datasets:
- -------------------------
Each attached dataset consists of four space-separated columns containing the
data on Age, Civil, Can/US and Income ($) respectively.
Dataset: Z
Information about the dataset
CLASSTYPE: numeric
CLASSINDEX: none specific

Income (target) | numeric | 662 unique values 0 missing | |

Age | numeric | 662 unique values 0 missing | |

Civil | numeric | 662 unique values 0 missing | |

Can/US | numeric | 662 unique values 0 missing |

Kappa coefficient achieved by the landmarker weka.classifiers.lazy.IBk -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

0.09

Second quartile (Median) of kurtosis among attributes of the numeric type.

30.22

Second quartile (Median) of means among attributes of the numeric type.

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.REPTree -L 3

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.DecisionStump

Second quartile (Median) of mutual information between the nominal attributes and the target attribute.

0.37

Second quartile (Median) of skewness among attributes of the numeric type.

Kappa coefficient achieved by the landmarker weka.classifiers.trees.DecisionStump

Minimal mutual information between the nominal attributes and the target attribute.

9.76

Second quartile (Median) of standard deviation of attributes of the numeric type.

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.RandomTree -depth 1

Maximum mutual information between the nominal attributes and the target attribute.

The minimal number of distinct values among attributes of the nominal type.

Error rate achieved by the landmarker weka.classifiers.trees.RandomTree -depth 1

Number of attributes needed to optimally describe the class (under the assumption of independence among attributes). Equals ClassEntropy divided by MeanMutualInformation.

The maximum number of distinct values among attributes of the nominal type.

2.01

Third quartile of kurtosis among attributes of the numeric type.

Kappa coefficient achieved by the landmarker weka.classifiers.trees.RandomTree -depth 1

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.J48 -C .00001

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.DecisionStump -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.RandomTree -depth 2

Third quartile of mutual information between the nominal attributes and the target attribute.

Error rate achieved by the landmarker weka.classifiers.trees.DecisionStump -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

Error rate achieved by the landmarker weka.classifiers.trees.RandomTree -depth 2

0.79

Third quartile of skewness among attributes of the numeric type.

Kappa coefficient achieved by the landmarker weka.classifiers.trees.DecisionStump -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

Kappa coefficient achieved by the landmarker weka.classifiers.trees.RandomTree -depth 2

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.J48 -C .0001

-0.04

First quartile of kurtosis among attributes of the numeric type.

17928.78

Third quartile of standard deviation of attributes of the numeric type.

Area Under the ROC Curve achieved by the landmarker weka.classifiers.bayes.NaiveBayes -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.RandomTree -depth 3

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.REPTree -L 1

Error rate achieved by the landmarker weka.classifiers.bayes.NaiveBayes -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

Error rate achieved by the landmarker weka.classifiers.trees.RandomTree -depth 3

Average mutual information between the nominal attributes and the target attribute.

First quartile of mutual information between the nominal attributes and the target attribute.

Kappa coefficient achieved by the landmarker weka.classifiers.bayes.NaiveBayes -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

Kappa coefficient achieved by the landmarker weka.classifiers.trees.RandomTree -depth 3

An estimate of the amount of irrelevant information in the attributes regarding the class. Equals (MeanAttributeEntropy - MeanMutualInformation) divided by MeanMutualInformation.

-0.2

First quartile of skewness among attributes of the numeric type.

Area Under the ROC Curve achieved by the landmarker weka.classifiers.lazy.IBk -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

Standard deviation of the number of distinct values among attributes of the nominal type.

Average number of distinct values among the attributes of the nominal type.

3.37

First quartile of standard deviation of attributes of the numeric type.

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.REPTree -L 2

Error rate achieved by the landmarker weka.classifiers.lazy.IBk -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W