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Bayesian Clustering for Email Campaign Detection Peter Haider & Tobias Scheffer University of Potsdam

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Bayesian Clustering for Email Campaign Detection. Peter Haider & Tobias Scheffer University of Potsdam. Email Campaign Detection. $drug1 $price1 $drug2 $quantity $price2 . - PowerPoint PPT Presentation

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Bayesian Clustering for Email Campaign DetectionPeter Haider & Tobias SchefferUniversity of Potsdam

1Email Campaign DetectionPeter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign DetectionHello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month. Dear Mr/Mrs, This is Brenda Dunn. Our office confirms you can get a $228.000 loan for a $371.00 per month payment.

$salutation, This is $firstname $lastname. Our $organisation confirms you $acceptance for a $volume loan for a $payment. Probabilistictemplates

Generatedexamples

Dear friend,nothing specific whatsoever.

$drug1 $price1 $drug2 $quantity $price2 .

2Email Campaign DetectionPeter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign Detection

Set of objectsCluster according totheir sources

Joint likelihood: integrate out parameters

Dear friend,nothing specific whatsoever.

Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month. Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month. Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month. Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month.

$salutation, This is $firstname $lastname. Our $organisation confirms you $acceptance for a $volume loan for a $payment.

$drug1 $price1 $drug2 $quantity $price2 .??Dear friend,nothing specific whatsoever.

3Spam FilteringPeter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign Detection

Clustered emails in spam trapIncoming emails

Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month. Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month.

Inbox: filter according to threshold on conditional likelihood

Dear friend,nothing specific whatsoever.

Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month. Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month. 4Problem SettingUnknown number of sources with hidden parameters.

Set of objects, generated from several sources.

Goal: Find most likely clustering of objects according to their source.Peter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign Detection

$salutation, This is $firstname $lastname. Our $organisation confirms you $acceptance for a $volume loan for a $payment.

$drug1 $price1 $drug2 $quantity $price2 .

Dear friend,nothing specific whatsoever.

Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month. Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month. Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month. Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month.

Dear friend,nothing specific whatsoever.

5OutlineReview: Closed-form solution for Bayesian clustering with independent binary features.Feature transformation that allows arbitrary dependencies in input space.Optimization problem and algorithm for learning feature transformation.Case study: Filtering spams through campaign detection.Peter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign Detection6Bayesian Clustering with Independent Binary FeaturesFactorize likelihood and prior over dimensions.

Analytical forms of joint likelihood and predictive probability.

Peter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign Detection

Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month. Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month. Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month. $salutation, This is $firstname $lastname. Our $organisation confirms you $acceptance for a $volume loan for a $payment. 7Feature TransformationIndependence assumption inappropriate.Transform features into different space, where dimensions are (more or less) independent.

Peter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign Detection

8How Do We Get ?Approximate true predictive distribution.

Ensure that approximation is suitable as probability distribution.

Peter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign Detection

9What Does Look Like?Construct from elementary Boolean operations.

Search space: all concatenationsIncludes all possible binary transformations.Injective, sparsity preserving.

Peter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign Detection

10Minimize expected Kullback-Leibler divergence between true and approximated predictive distribution:

Approximate expectation by sum over empirical sample S:Optimization problem:

How To Find The Optimal ?Peter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign Detection

11Feature Transformation: AlgorithmNon-convex optimization problem greedy procedure.Algorithm:Start with identity transformationRepeat Until convergence.

Peter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign Detection

12

Feature Transformation: ExamplePeter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign Detection

13Sequential Bayesian ClusteringPeter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign DetectionCluster according totheir sources

Dear friend,nothing specific whatsoever.

Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month. Hello, This is Terry Hagan. Our company confirms you are legible for a $250.000 loan for a $380.00/month.

Each step: most likely cluster 14Case Study: Email Campaign DetectionGenerally: no ground truth for unsupervised clustering.Natural evaluation criterion for email campaign detection: contribution to accurate filtering of spam.

Peter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign Detection

Spam trap stream: window of 5,000 most recent spams total: 69,625 sequential clustering of window.

Test stream:mixture of 62,662 spams 36914 non-spamsDecision criterion:

15Setting 1: Non-Spams from Test Distribution AvailableNon-spams for training: 10,000 emails from same distribution as test non-spams.Optimistic setting, since in practice test distribution differs from training distribution.Compare:

Peter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign DetectionBayesian ClusteringBayesian ClusteringSupport Vector MachineFeature Transformation trained on 10,000 non-spamsNo Feature TransformationTrain on 10,000 non-spams and window of 5,000 most recent trapped spams16

ResultsTune hyperparameters for maximum number of true positives at zero false positives.

Increase of true positive rate with Bayesian clustering with feature transformation over SVM.Peter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign Detection17Setting 2: No Non-Spams from Test Distribution AvailableNo non-spams for training.Evaluate performance on entirely unknown non-spams.

Compare:

Peter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign DetectionBayesian ClusteringBayesian ClusteringOne-class SVMFeature Transformation trained on 10,000 spamsNo Feature TransformationTrain on window of 5,000 most recent trapped spams18ResultsTune hyperparameters for maximum number of true positives at zero false positives.

Sevenfold increase of true positive rate with Bayesian clustering with feature transformation over SVM.

Peter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign Detection

19ConclusionsDerived closed-form solution for Bayesian clustering, allowing arbitrary dependencies in input space.Optimization problem for learning feature transformation as set of Boolean functions, that minimizes approximation error.Spam filtering case study showed vast improvements over SVM in absence of non-spam training examples from the test distribution.Peter Haider & Tobias Scheffer: Bayesian Clustering for Email Campaign Detection20


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