This document summarizes a presentation on designing robust classifiers for adversarial environments given at the 2011 IEEE International Conference on Systems, Man, and Cybernetics. The presentation introduces an approach to model potential attacks at test time using a probabilistic model of the data distribution under attack. This model is then used to design classifiers that are more robust to attacks. Experimental results on biometric identity verification and spam filtering show that the proposed approach can increase classifier security against attacks while maintaining accuracy.

1. 2011 IEEE Int’l Conf. on Systems, Man, and Cybernetics (SMC2011)
Special Session on Machine Learning, 9-12/10/2011, Anchorage, Alaska
Design of robust classifiers for
adversarial environments
Battista Biggio, Giorgio Fumera, Fabio Roli
PRAgroup
Pattern Recognition and Applications Group
Department of Electrical and Electronic Engineering (DIEE)
University of Cagliari, Italy

2. Outline
• Adversarial classification
– Pattern classifiers under attack
• Our approach
– Modelling attacks to improve classifier security
• Application examples
– Biometric identity verification
– Spam filtering
• Conclusions and future works
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3. Adversarial classification
• Pattern recognition in security applications
– spam filtering, intrusion detection, biometrics
• Malicious adversaries aim to evade the system
x2 legitimate
f(x)
malicious
Buy viagra!
Buy vi4gr@!
x1
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4. Open issues
1. Vulnerability identification
2. Security evaluation of pattern classifiers
3. Design of secure pattern classifiers
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5. Our approach
• Rationale
– to improve classifier security (robustness) by modelling
data distribution under attack
• Modelling potential attacks at testing time
– Probabilistic model of data distribution under attack
• Exploiting the data model for designing more
robust classifiers
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6. Modelling attacks at test time
Two class problem
Y
Attack X is the feature vector
Y is the class label:
X legitimate (L)
malicious (M)
P(X,Y ) = P(Y )P(X | Y )
In adversarial scenarios, attacks can influence X and Y
Oct. 10, 2011 Design of robust classifiers for adversarial environments - F. Roli - SMC2011 6

7. Manipulation attacks against anti-spam filters
•Text classifiers in spam filtering
binary features (presence / absence of keywords)
•Common attacks
bad word obfuscation (BWO) and good word insertion (GWI)
Buy viagra! Buy vi4gr4!
Did you ever play that game
when you were a kid where the
little plastic hippo tries to
gobble up all your marbles?
x = [0 0 1 0 0 0 0 0 …] x’ = [0 0 0 0 1 0 0 1 …]
x ' = A(x)
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8. Modelling attacks at test time
Y
Attack
X
P(X,Y ) = P(Y )P(X | Y )
In adversarial scenarios, attacks can influence X and Y
We must model this influence to design robust classifiers
Oct. 10, 2011 Design of robust classifiers for adversarial environments - F. Roli - SMC2011 8

9. Modelling attacks at test time
A Y
P(X,Y , A) = P(A)P(Y | A)P(X | Y , A)
X
• A is a r.v. which indicates whether the sample is
an attack (True) or not (False)
• Y is the class label: legitimate (L), malicious (M)
• X is the feature vector
Oct. 10, 2011 Design of robust classifiers for adversarial environments - F. Roli - SMC2011 9

10. Modelling attacks at test time
Ptr (X,Y = L) Ptr (X,Y = M )
Training time
x
Pts (X,Y = M ) =
Pts (X,Y = L) Pts (X,Y = M | A = T )P(A = T ) + Pts (X,Y = M , A = F)
Testing time
x
Attacks which were not present at training phase!
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11. Modelling attacks at testing time
• Attack distribution
– P(X,Y=M, A=T) = P(X|Y=M,A=T)P(Y=M|A=T)P(A=T)
• Choice of P(Y=M|A=T)
– We set it to 1, since we assume the adversary has only
control on malicious samples
• P(A=T) is thus the percentage of attacks among malicious
samples
– It is a parameter which tunes the security/accuracy trade-
off
– The more attacks are simulated during the training phase,
the more robust (but less accurate when no attacks) the
classifier is expected to be at testing time
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12. Modelling attacks at testing time
Key issue:
modelling Pts(X, Y=M / A=T)
Pts (X,Y = L)
Pts (X,Y = M , A = F)
Testing time
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13. Modelling attacks at testing time
• Choice of Pts(X, Y=M / A=T)
– Requires application-specific knowledge
– Even if knowledge about the attack is available, still difficult
to model analytically
– An agnostic choice is the uniform distribution
Pts (X,Y = M ) =
Pts (X,Y = L) Pts (X,Y = M | A = T )P(A = T ) + Pts (X,Y = M , A = F)
Testing time
x
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14. Experiments
Spoofing attacks against biometric systems
• Multi-modal biometric verification systems
– Spoofing attacks
Fake fingerprints
Claimed
identity
Face Fingerprint
matcher matcher
s1 s2
Photo attack
Fusion module
Genuine / Impostor
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15. Experiments
Multi-modal biometric identity verification
true
genuine
s1
Sensor Face matcher
s
Score fusion rule s ! s"
s2 f (s1 , s2 )
Sensor Fingerprint matcher
false
impostor
• Data set
– NIST Biometric Score Set 1 (publicly available)
• Fusion rules
p(s1 | G)p(s2 | G)
– Likelihood ratio (LLR) s=
p(s1 | I )p(s2 | I )
– Extended LLR
[Rodrigues et al., Robustness of multimodal biometric fusion methods against spoof attacks,
JVLC 2009]
– Our approach (Uniform LLR)
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16. Remarks on experiments
•The Extended LRR [Rodrigues et al., 2009] used for
comparison assumes that the attack distribution is
equal to the distribution of legitimate patterns
Pts (X,Y = L) = Pts (X,Y = M | A = T )
Pts (X,Y = M , A = F)
Testing time
•Our rule, uniform LRR, assumes a uniform distribution
Experiments are done assuming that attack patterns
are exact replicas of legitimate patterns (worst case)
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17. Experiments
Multi-modal biometric identity verification
• Uniform LLR under fingerprint spoofing attacks
– Security (FAR) vs accuracy (GAR) for different P(A=T)
values
– No attack (solid) / under attack (dashed)
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18. Experiments
Multi-modal biometric identity verification
• Uniform vs Extended LLR under fingerprint
spoofing
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19. Experiments
Spam filtering
• Similar results obtained in spam filtering
– TREC 2007 public data set
– Naive Bayes text classifier
– GWI/BWO attacks with nMAX modified words per spam
AUC10%
TP
0 0.1 FP
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20. Conclusions and future works
• We presented a general generative approach
for designing robust classifiers against attacks at
test time
• Reported results show that our approach allow
to increase the robustness (i.e., the security) of
classifiers
• Future work
– To test Uniform LLR against more realistic spoof attacks
• Preliminary result: worst-case assumption is too pessimistic!
Biggio, Akhtar, Fumera, Marcialis, Roli, “Robustness of multimodal biometric
systems under realistic spoof attacks”, IJCB 2011
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