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KDD 2004:
Adversarial
Classification
Dalvi, Domingos, Mausam,
Sanghai, Verma
University of Washington
Introduction

Paper views classification as a game
between classifier and the adversary
 Data
is actively manipulated by the adversary
to make classifier produce false negatives

Proposes a (Naïve Bayes) classifier that is
optimal given adversary’s optimal strategy
Motivation (1)


Many (all) data-mining algorithms assume that
data-generating process is independent of
classifier’s activities
This is not true in domains like
 Spam detection
 Intrusion detection
 Fraud detection
 Surveillance
Where data is actively manipulated by an
adversary seeking to make classifier produce
false negatives
Motivation (2)
In real world performance of classifier can
degrade rapidly after deployment as
adversary learns how to defeat it
 Solution: repeated, manual, ad hoc
reconstruction of the classifier
 This problem is different from a concept
drift, since data is actively manipulated – is
a function of the classifier itself

Outline
Problem definition
 For Naïve Bayes:

 Optimal
strategy for adversary against
adversary-unaware classifier
 Optimal strategy for classifier playing against
adversary

Experimental results on 2 email spam
datasets
Problem definiton
X = (X1, X2, … Xn) a set of features
 Instance space X. Instance x X has
feature values xi
 Instances belong to 2 classes:

 Positive
(malicious) are i.i.d. from P(X|+)
 Negative (innocent) are i.i.d. from P(X|–)

Training set S, test set T
A game between 2 players:
Classifier tries to learn a function
yC = C(x)
that will correctly predict classes
 Adversary attempts to make Classifier
classify positive (harmful) instances as
negative by modifying an instance x:
x’ = A(x)

(note: adversary can not modify negative, ie.
non-spam, instances)
Cost/Utilities for Classifier
Vi: cost of measuring feature Xi
 UC(yC, y): utility of classifying instance as
yC having true class y
 Typically:

–) < 0,
 UC(+, +) > 0,
 UC(+,
UC(–, +) < 0
UC(–, –) > 0
makes an error
correct classification
Cost/Utilities for Adversary
Wi(xi, x’): cost of changing ith feature from
xi to xi’
 UA(yC, y): utility accrued by adversary
when classifier classifyes yc an instance of
class y.
 Typically:

 UA(–,
spam get through
+) > 0
spam in detected
 UA(+, +) < 0
don’t care about non-spam
 UA(+, –) = 0, UA(–, –) = 0
Goal of Classifier

Wants to build classifier C that will
maximize expected utility taking into
account adversaries actions:
utility given
modified data
cost for observing
a feature
Goal of Adversary

Wants to find feature change strategy that
will maximize utility given the costs:
utility given
modified data
cost of changing
the features
The game


We assume that all parameters of both players
are known to each other
Game operates:
1.
2.
3.
4.
Classifier starts assuming data in unaltered
Adversary deploys optimal plan A(x) against
classifier
Classifier deploys optimal classifier C(A(x)) against
adversary
...
Classifier: No Adversary

Naïve Bayes:

Bayes’ optimal prediction given utility
matrix for instance x is the class yC that
maximizes:
prediction
expected utility
Adversary strategy

Adversary assumes:
 complete
information
 classifier is unaware of adversary

Naïve Bayes classifies x as positive if:
Naïve Bayes

Modify features so that
 inequality
does not hold
 the cost is lower than expected utility

Boils down to a integer linear program
Classifier with Adversary

Classifier assumes:
training set is drawn
from the real distribution
 Adversary uses optimal strategy
 Training set is not tampered by Adversary


Maximize conditional utility:
The only change is:



adversary modifies only positive examples
It will not modify example if: classifier’s prediction is negative, or
transformation is to costly
Naïve algorithm: for all positive examples and find probability
they are modified
Experiments

2 datasets:
 Ling-Spam:
2412 non-spam, 481 spam
 Email-Data: 642 non-spam, 789 spam

Scenarios:
 Add
words: adversary is adding words. Cost of adding
a word is 1. (Adding unnecessary words)
 Add length: same as Add words, except cost is
proportional to word length. (Spammer is paying for
data transfer)
 Synonyms: replace existing word with its synonym.
(Spammer does not want to alter the content)
Utility matrix





UA: adversary
UC: classifier
prediction
true class
+: spam
–: no spam
Scenarios:
 AddWords: can add max 20 words
 AddLength: can add max 200 characters
 Synonmy: can change max 20 synonyms
False positives and False negatives




By increasing UC we observe expected behavior
AC never produces False Positive
so average utility stays the same
Adversary “helps” classifier to reduce FPs, because
adversary is unlikely to send spam unaltered. So nonspam messages (unaltered) will now be classified as
negative.
Further work / Conclusions

Further work:
 Repeated
game
 Incomplete information
 Approximately optimal strategies
 Generalization to other classifiers

Conclusions:
 Formalized
the problem of adversarial
manipulation
 Extended Naïve Bayes classifier
 Outperforms standard technique
Other interesting papers (1)

Best Paper: Probabilistic Framework for
Semi-Supervised Clustering by Basu,
Bilenko, and Mooney:
 gives
a probabilistic model to find clusters that
respect "must-link" and "cannot-link"
constraints
 the EM-type algorithm is an incremental
improvement over previous methods
Other interesting papers (2)

Data Mining in Metric Space: An Empirical
Analysis of Supervised Learning Performance
Criteria by Caruana and Niculescu-Mizil:
a
massive comparison of different learning methods
with different binary datasets, on different measure of
performance: accuracy given a threshold, area under
the ROC curve, squared error, etc.
 measures that depend on ranking only, and measures
that depend on scores being calibrated probabilities,
form two clusters.
 maximum margin methods (SVMs and boosted trees)
give excellent ranking but scores that are far from
well-calibrated probabilities.
 squared error may be the best general-purpose
measure.
Other interesting papers (3)

Cyclic Pattern Kernels for Predictive
Graph Mining by Horvath, Gaertner, and
Wrobel:
 kernel
for classifying graphs based on cyclic
and tree patterns
 Computationally efficient (does not suffer
frequent sub-graphs limitations)
 they use it with SVM for classifying molecules