by ankur khator 01005028 gaurav sharma 01005029 arpit mathur 01d05014 spam filtering
TRANSCRIPT
ByAnkur Khator 01005028Gaurav Sharma 01005029Arpit Mathur 01D05014
SPAM FILTERING
“junk email” or “unsolicited commercial email”.
Spam filtering - a special case of email classification.
Only 2 classes – Spam and Non-spam.
What is Spam Email?
Various Approaches
Bayesian Learning Probabilistic model for Spam Filtering Bag of Words Representation
Ripper algorithm Context Sensitive Learning.
Boosting algorithm Improving Accuracy by combining weaker
hypotheses.
Term Vectors
Naive Bayes for Spam
Seeking model to find
P(Y=1/X1=x1,X2=x2,..,Xd=xd)
From Bayes theorem
P(Y=1/X1=x1,..,Xd=xd) = P(Y=1) * P(X1=x1,..,Xd=xd/Y=1)
P(X1=x1,..Xd=xd)
P(Y=0/X1=x1,..,Xd=xd) = P(Y=0) * P(X1=x1,..,Xd=xd/Y=0)
P(X1=x1,..Xd=xd)
Justification of using Bayes Theorem Sparseness of data P(B/A) can be easily and accurately
determined as compared to P(A/B)
Assume P(X1=x1,..,Xd=xd/Y=k) = ∏ P(Xi=xi / Y=k)
Naive Bayes for Spam(contd.)
Also assume Xi = 1 if no of occurrence of word i >= 1
= 0 otherwise
referred to as weights of evidence
• Inconsistency when some probability is zero.
•Smooth the estimates by adding a smooth positive constant to both numerator and denominator of each probability estimate
Naive Bayes for Spam(contd.)
Assume new mail with text “The quick rabbit rests”
Classifying
0.51 + 0.51 + 0 + 0.51 + 1.10 + 0 = 2.63
Probability = 0.93
Threshold
Lower threshold Higher false positive rate
Higher threshold Higher false negative rate Preferred
Linear Classifier Ignores the effect of Context of word on its meaning.
Unrealistic . Build a linear classifier that test for more complex Features like Simultaneous Occurrences. High Computation Cost !! Non-Linear Classification is the Solution
Non-Linear Classification
Ripper
Disjunction of Different Contexts Each Contexts is conjunction of Simple terms Context of w1 is :
if w2 belongs to data and w3 belongs to data.
i.e. for context to be true w1 must occur with w2 and w3.
Three Components of Ripper Algorithm:
Rule Learning :
Spam spam Є Subject Spam Free Є Subject ,Spam Є Subject. Spam Gift!! Є Subject, Click Є Subject. The rule would be disjunction of three
statements stated above. There is an initial set of rules too
Constructing Rule Set
Initial Rule Set is Constructed Using a greedy Strategy.
Based on the IREP (Incremental Reduced Error Pruning)
To Construct A new Rule partitioning Dataset into two parts training Set And Pruning Set is Done.
Every Time a Single condition is Added to Rule.
Simplification And Optimization
At every step the density of +ve examples covered is increased.
Adding stops until clause cover no –ve example or there is no positive gain.
After this, pruning i.e. simplification is done. At every stage, again following greedy Strategy
Reaching Sufficient Rules The clause is deleted which maximizes the Function
where U+(i+1) and U-
(i-1) are the positive and negative examples.
Termination when information gain is non-zero i.e. every rule covers +ve examples.
But If data is noisy then number of rules increase
MDL
Several heuristics are applied to solve the problem. MDL(Minimum Description Length) is one of them.
After addition of each rule , total length of current rule set and example is calculated.
Addition of rule is stopped when this length is d bits larger than shortest length.
AdaBoost
Easy to find rule of thumb which are often correct
If ‘buy now’ occurs in message, then predict ‘spam’
Hard to find one rule which is very accurate AdaBoost helps here
general method of converting rough rules of thumb into highly accurate prediction rule
Concentrating on hard examples
Pictorially
Algorithm Input S = { (Xi , Yi) } m
i=1
Initialize D(i) = 1/m for all i For i = 1 to T
H(t) = WeakLearner(S,Dt) Choose βt
ln((1-ε)/ε) (proven to Minimize error for 2class) [2]
Update Dt+1(i) = Dt(i) exp(-βtYiht(xi)) and Normalize
Final Hypotheses f(x) = ∑βt ht(x)
Example
Example
Accuracy Weighted accuracy measure
(λL- + S+) / (λL + S) λ strictness measure L : # legitimate messages S : # spam L- : #legitimate messages classified as legitimate S+ : #spam classified as spam
Improving accuracy Increase λ Introduce θ threshold
Example classified positive only if f(x) > θ Default is ZERO
Recall correctly predicted spam out of number of spam in corpus
Precision correctly classified spam out of number predicted as spam
Results on corpus PU1 . . . [1]
T RECALL PRECISION ACC
Tree Depth 1
Θ = 10.2 λ = 9525 93.55 98.71 98.59
Tree Depth 1
θ = 46.9 λ = 999550 74.43 100 99.98
Tree Depth 5
θ = 37.4 λ = 9 525 93.97 99.12 98.92
Tree Depth 5
Θ = 178 λ = 999550 66.53 100 99.97
Pros and Cons Fast and Simple No parameters to tune Flexible
Can combine with any learning Algorithm No knowledge needed of WeakLearner
Error reduces exponentially Robust to overfitting Data Driven – requires lots of data Performance depends on WeakLearner
May fail if WeakLearner is too weak
Conclusion
RIPPER as text categorization algorithm works better than Naïve Bayes (better for more classes).
Comparable for spam filtering (2 classes) Boosting better than any weak learner it
works on.
References
[1] Boosting trees for Anti Spam Email Filtering by Xavier Carreras and Llius Marquez 2001.
[2] The boosting approach to machine learning: An overview. by Robert E. Schapire in MSRI Workshop on Nonlinear Estimation and Classification, 2002.
[3] Statistics and The War on Spam by David Madigan, David Madigan, 2004.
[4] Androutsopoulos, J. Koutsias, K. V. Chandrinos, G. Paliouras, and C. D. Spyropoulos. An Evaluation of Naive Bayesian Anti-Spam Filtering. In Proc. of the workshop on Machine Learning in the New Information Age, 2000. http://citeseer.ist.psu.edu/androutsopoulos00evaluation.html
[5] William W. Cohen, Yoram Singer: Context-sensitive Learning Methods for Text Categorization. SIGIR 1996: 307-315