Fraud Detection by Stacking Cost-Sensitive Decision Trees
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Worldwide, billions of euros are lost every year due to credit card fraud. Increasingly, fraud has diversified to different digital channels, including mobile and online payments, creating new challenges as innovative new fraud patterns emerge. Hence, it remains challenging to find effective methods of mitigating fraud. Existing solutions include simple if-then rules and classical machine learning algorithms. Credit card fraud is by definition an example-dependent and cost-sensitive classification problem, in which the costs due to is classification vary between examples and not only within classes, i.e., misclassifying a fraudulent transaction may have a financial impact ranging from a few to thousands of euros. In this paper, we propose an extension to the cost-sensitive decision trees algorithm, by creating an ensemble of such trees, and combining them using a stacking approach with a cost-sensitive logistic regression. We compare our method with standard machine learning algorithms and state-of-the-art cost-sensitive classification methods using a real credit card fraud dataset provided by a large European card processing company. The results show that our method achieves savings of up to 73.3%, more than 2 percentage points more than a single cost-sensitive decision tree.
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Fraud Detection by Stacking Cost-Sensitive Decision Trees
- 1. Fraud Detection by Stacking Cost-Sensitive Decision Trees Alejandro Correa Bahnsen, PhD Chief Data Scientist & Head of Research acorrea@easysol.net
- 2. Who am I? Chief Data Scientist at Easy Solutions Industrial Engineer PhD in Machine Learning from Luxembourg University Scikit-Learn contributor Organizer of Science Bogota Meetups 2
- 3. AboutEasySolutions® 3 A leading global provider of electronic fraud prevention for financial institutions and enterprise customers 430+ customers In 30 countries 115 million Users protected 30 billion Online connections monitored Industry recognition
- 4. TotalFraudProtection Discuss what makes a data science project successful 4
- 5. 5 Risk Based Authentication Phishing URL Classification Phishing Brand ID Fraud Detection 19h risk = 10 9h risk = 95 HTML Injection Biometrics
- 6. Research/ DataScienceSpectrum 6 • Maybe someday, someone can use this Basic Research • I might be able to use this Applied Research • I can use this (sometimes) Working Prototype • Software engineers can use thisQuality Code • People can use this Tool or Service Innovation practicality
- 7. Credit Card Fraud Detection 7
- 8. Estimate the probability of a transaction being fraud based on analyzing customer patterns and recent fraudulent behavior Issues when constructing a fraud detection system: • Skewness of the data • Cost-sensitivity • Short time response of the system • Dimensionality of the search space • Feature preprocessing • Model selection Creditcardfrauddetection 8
- 10. • Larger European card processing company • 2012 & 2013 card present transactions • 20MM Transactions • 40,000 Frauds • 0.467% Fraud rate • ~ 2MM EUR lost due to fraud on test dataset Dec Nov Oct Sep Aug Jul Jun May Apr Mar Feb Jan Test Train Data
- 11. Raw features 11 Attribute name Description Transaction ID Transaction identification number Time Date and time of the transaction Account number Identification number of the customer Card number Identification of the credit card Transaction type ie. Internet, ATM, POS, ... Entry mode ie. Chip and pin, magnetic stripe, ... Amount Amount of the transaction in Euros Merchant code Identification of the merchant type Merchant group Merchant group identification Country Country of trx Country 2 Country of residence Type of card ie. Visa debit, Mastercard, American Express... Gender Gender of the card holder Age Card holder age Bank Issuer bank of the card Features
- 12. Credit card fraud detection is a cost-sensitive problem. As the cost due to a false positive is different than the cost of a false negative. • False positives: When predicting a transaction as fraudulent, when in fact it is not a fraud, there is an administrative cost that is incurred by the financial institution. • False negatives: Failing to detect a fraud, the amount of that transaction is lost. Moreover, it is not enough to assume a constant cost difference between false positives and false negatives, as the amount of the transactions varies quite significantly. 12 FinancialEvaluation
- 13. Cost matrix 𝐶𝑜𝑠𝑡 𝑓 𝑆 = 𝑖=1 𝑁 𝑦𝑖 𝑐𝑖 𝐶 𝑇𝑃 𝑖 + 1 − 𝑐𝑖 𝐶 𝐹𝑁 𝑖 + 1 − 𝑦𝑖 𝑐𝑖 𝐶 𝐹𝑃 𝑖 + 1 − 𝑐𝑖 𝐶 𝑇𝑁 𝑖 13 Actual Positive 𝒚𝒊 = 𝟏 Actual Negative 𝒚𝒊 = 𝟎 Predicted Positive 𝒄𝒊 = 𝟏 𝐶 𝑇𝑃 𝑖 = 𝐶 𝑎 𝐶 𝐹𝑃 𝑖 = 𝐶 𝑎 Predicted Negative 𝒄𝒊 = 𝟎 𝐶 𝐹𝑁 𝑖 = 𝐴𝑚𝑡𝑖 𝐶 𝑇𝑁 𝑖 = 0 FinancialEvaluation
- 14. • Cost Proportionate Sampling • Bayes minimum risk • Cost-sensitive logistic regression • Cost-sensitive decision trees • Stacking Cost-sensitive decision trees CostSensitiveAlgorithms 14
- 15. CostProportionateSampling Normalized Cost weight 𝑤𝑖 = 𝐶 𝐹𝑃 𝑖 𝑖𝑓 𝑦𝑖 = 0 𝐶 𝐹𝑁 𝑖 𝑖𝑓 𝑦𝑖 = 1 𝑤𝑖 = 𝑤𝑖 max 𝑗 𝑤𝑗
- 16. CostProportionateSampling Cost Proportionate Over Sampling Example 𝑦𝑖 𝑤𝑖 1 0 1 2 1 10 3 0 2 4 1 20 5 0 1 Initial Dataset (1,0,1) (2,1,10) (3,0,2) (4,1,20) (5,0,1) Cost Proportionate Dataset (1,0,1) (2,1,1), (2,1,1), …, (2,1,1) (3,0,2), (3,0,2) (4,1,1), (4,1,1), (4,1,1), …, (4,1,1), (4,1,1) (5,0,1) *Elkan, C. (2001). The Foundations of Cost-Sensitive Learning.
- 17. CostProportionateSampling Cost Proportionate Rejection Sampling Example 𝑦𝑖 𝑤𝑖 1 0 1 2 1 10 3 0 2 4 1 20 5 0 1 Cost Proportion ate Dataset (2,1,1) (4,1,1) (4,1,1) (5,0,1) *Zadrozny et al. (2003). Cost-sensitive learning by cost-proportionate example weighting. 𝑤𝑖/max( 𝑤𝑖) 0.05 0.5 0.1 1 0.05 Initial Dataset (1,0,1) (2,1,10) (3,0,2) (4,1,20) (5,0,1)
- 18. Decision model based on quantifying tradeoffs between various decisions using probabilities and the costs that accompany such decisions Risk of classification 𝑅 𝑐𝑖 = 0|𝑥𝑖 = 𝐶 𝑇𝑁 𝑖 1 − 𝑝𝑖 + 𝐶 𝐹𝑁 𝑖 ∙ 𝑝𝑖 𝑅 𝑐𝑖 = 1|𝑥𝑖 = 𝐶 𝐹𝑃 𝑖 1 − 𝑝𝑖 + 𝐶 𝑇𝑃 𝑖 ∙ 𝑝𝑖 Using the different risks the prediction is made based on the following condition: 𝑐𝑖 = 0 𝑅 𝑐𝑖 = 0|𝑥𝑖 ≤ 𝑅 𝑐𝑖 = 1|𝑥𝑖 1 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 18 BayesMinimumRisk
- 19. • Logistic Regression Model • Cost Function • Cost Analysis Cost-Sensitive- LogisticRegression
- 20. • Actual Costs • Cost-Sensitive Function Cost-Sensitive- LogisticRegression
- 21. 21 Proposed Cost based impurity measure 𝑆 𝑙 = 𝑥|𝑥𝑖 ∈ 𝑆 ∧ 𝑥𝑖 𝑗 ≤ 𝑙 𝑚 𝑗 𝑆 𝑟 = 𝑥|𝑥𝑖 ∈ 𝑆 ∧ 𝑥𝑖 𝑗 > 𝑙 𝑚 𝑗 • The impurity of each leaf is calculated using: 𝐼𝑐 𝑆 = min 𝐶𝑜𝑠𝑡 𝑓0 𝑆 , 𝐶𝑜𝑠𝑡 𝑓1 𝑆 𝑓 𝑆 = 0 𝑖𝑓 𝐶𝑜𝑠𝑡 𝑓0 𝑆 ≤ 𝐶𝑜𝑠𝑡 𝑓1 𝑆 1 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 • Afterwards the gain of applying a given rule to the set 𝑆 is: 𝐺𝑎𝑖𝑛 𝑐 𝑥 𝑗, 𝑙 𝑚 𝑗 = 𝐼𝑐 𝜋1 − 𝐼𝑐 𝜋1 𝑙 + 𝐼𝑐 𝜋1 𝑟 S S S 𝑥 𝑗, 𝑙 𝑚 𝑗 Cost-SensitiveDecisionTrees
- 22. 22 Decision trees construction • The rule that maximizes the gain is selected 𝑏𝑒𝑠𝑡 𝑥, 𝑏𝑒𝑠𝑡𝑙 = 𝑎𝑟𝑔 max 𝑗,𝑚 𝐺𝑎𝑖𝑛 𝑥 𝑗, 𝑙 𝑚 𝑗 S S S S S S S S S S S • The process is repeated until a stopping criteria is met: Cost-SensitiveDecisionTrees
- 23. 23 Proposed cost-sensitive pruning criteria • Calculation of the Tree savings and pruned Tree savings S S S S S S S S S S S 𝑃𝐶𝑐 = 𝐶𝑜𝑠𝑡 𝑓 𝑆, 𝑇𝑟𝑒𝑒 − 𝐶𝑜𝑠𝑡 𝑓 𝑆, 𝐸𝐵 𝑇𝑟𝑒𝑒, 𝑏𝑟𝑎𝑛𝑐ℎ 𝑇𝑟𝑒𝑒 − 𝐸𝐵 𝑇𝑟𝑒𝑒, 𝑏𝑟𝑎𝑛𝑐ℎ • After calculating the pruning criteria for all possible trees. The maximum improvement is selected and the Tree is pruned. • Later the process is repeated until there is no further improvement. S S S S S S S S S S S S S S Cost-SensitiveDecisionTrees
- 24. Typical ensemble is made by combining T different base classifiers. Each base classifiers is trained by applying algorithm M in a random subset 24 𝑀𝑗 ← 𝑀 𝑆𝑗 ∀𝑗 ∈ 1, … , 𝑇 EnsembleCost-SensitiveDecisionTrees
- 25. 25 1 2 3 4 5 6 7 8 8 6 2 5 2 1 3 6 7 1 2 3 8 1 5 8 1 4 4 2 1 9 4 6 1 1 5 8 1 4 4 2 1 1 5 8 1 4 4 2 1 1 5 8 1 4 4 2 1 Bagging Pasting Random forest Random patches Training set EnsembleCost-SensitiveDecisionTrees
- 26. After the base classifiers are constructed they are typically combined using one of the following methods: • Majority voting 𝐻 𝑆 = 𝑓𝑚𝑣 𝑆, 𝑀 = 𝑎𝑟𝑔 max 𝑐∈ 0,1 𝑗=1 𝑇 1 𝑐 𝑀𝑗 𝑆 26 EnsembleCost-SensitiveDecisionTrees
- 27. • Proposed cost-sensitive stacking 𝐻 𝑆 = 𝑓𝑠 𝑆, 𝑀, 𝛽 = 1 1 + 𝑒 − 𝑗=1 𝑇 𝛽 𝑗 𝑀 𝑗 𝑆 Using the cost-sensitive logistic regression [Correa et. al, 2014] model: 𝐽 𝑆, 𝑀, 𝛽 = 𝑖=1 𝑁 𝑦𝑖 𝑓𝑠 𝑆, 𝑀, 𝛽 𝐶 𝑇𝑃 𝑖 − 𝐶 𝐹𝑁𝑖 + 𝐶 𝐹𝑁 𝑖 + 1 − 𝑦𝑖 𝑓𝑠 𝑆, 𝑀, 𝛽 𝐶 𝐹𝑃 𝑖 − 𝐶 𝑇𝑁 𝑖 + 𝐶 𝑇𝑁 𝑖 Then the weights are estimated using 𝛽 = 𝑎𝑟𝑔 min 𝛽 𝐽 𝑆, 𝑀, 𝛽 27 EnsembleCost-SensitiveDecisionTrees
- 28. 0% 10% 20% 30% 40% 50% 60% 70% 80% Expert Rules Random Forests RF CS Sampling CS Logistic Regression CS Decision Tree Ensemble CSDT Majority Ensemble CSDT Stacking % Savings F1-Score Results 28
- 31. • New framework for stacking of example dependent cost-sensitive decision trees • Models should be evaluated taking into account real financial costs of the application • Algorithms should be developed to incorporate those financial costs Conclusions 31
- 32. Any questions or comments, please let me know. Alejandro Correa Bahnsen, PhD Chief Data Scientist & Head of Research acorrea@easysol.net Thank you!