代写ST309 – Exercise 6帮做Python程序

ST309 – Exercise 6

This counts for 10% of the final assessment of the course.

The marks in brackets reflect marks for each question.

Please submit your solutions in a pdf file to Moodle by the noon (UK time) of Friday, 13 December 2024. Late submission entails penalties: 5 marks (out of maximum 100) will be deducted for every half-day (12 hours) within the first 24 hours after the deadline, and 5 marks will be deducted for each further 24 hours. Submissions are not accepted after 5pm on Wednesday, 18 December 2024.

You should only submit your own work, and cannot use materials from the past and/or your classmates. Plagiarism is a very serious ofense that is quite easy to detect.  It will result in instant failure (mark 0).

This exercise is on credit card fraud detection based on a data set downloaded from Kaggle Datasets at

https://www.kaggle.com/mlg-ulb/creditcardfraud

Background information on the data is available at

https://www.kaggle.com/mlg-ulb/creditcardfraud/home

Previous attempts can be found at

https://www.kaggle.com/janiobachmann/credit-fraud-dealing-with-imbalanced-datasets/versions (All those analysis was done using Python.  But you should be able to follow the ideas, understand most the results. Especially some initial data exploration is easy to follow.)

The dataset contains 284,807 credit card transactions in two days in September 2013 by European card- holders, of which 492 are frauds.  So the data is highly unbalanced:  the positive cases (i.e.  frauds) account for merely 0.172% of all transactions.

Due to the confidentiality issues, the original features for each transaction are masked via a linear transfor- mation.  The 28 transformed features are presented as V1, V2, · · · , V28.  According to the  above webpage, those 28 features are the principal components of the original features.  No further information on those features is provided. In addition to those 28 variables, there are 3 untransformed variables:

• Time: number of seconds elapsed between each transaction and the first transaction in the dataset

• Amount: the amount of the transaction

•  Class: binary label with value 1 for ‘fraud’ and 0 otherwise.

The whole dataset has 284,807 rows and 31 columns.  The task is to build up efective algorithms for detecting fraudulent credit card transactions.

The  data is  extremely  imbalanced with  only 0.172%  ‘positives’  (i.e.   frauds).   Hence  the  information on frauds is overwhelmed by that on true and genuine transactions.  This imbalance leads the fitted models using the whole data predominately led by the information on ‘negatives’, and the signal on ‘positives’ is too weak to be picked up.  To balance the information used in building classifiers, we have created a more balanced but, unfortunately, much smaller training data with 24.62% positive cases, and also a testing data set which is about equally imbalanced as the whole data set.

•  creditCardTrain.csv: of size 1592×31, consisting of 1200 randomly selected non-fraudulent transactions plus 392 randomly selected fraud transactions. The true positive rate is about 24.62%.

•  creditCardTest .csv: of size 57889 × 31, consisting of 57789 randomly selected non-fraudulent transac- tions plus  100 remaining fraud transactions.  It has no overlaps with  creditCardTrain .csv.  The true positive rate is 0.173%.

The two data sets are placed on the course Moodle page.  For your information, I attach below the codes for constructing those two data sets.

> library(readr); library(dplyr)

> CC=read_csv("creditcard .csv")  # read_csv is a much faster version of read .csv

> CC1=CC[CC$Class==1,]  # extract all frauds

> dim(CC1)

[1] 492  31

> train1=sample(1:492, 392)

> CC1train=CC1[train1,]

> CC1test=CC1[-train1,]

> CC0=CC[CC$Class==0,]  # extract all genuine transactions

> dim(CC0)

[1] 284315     31

> train0=sample(1:284315, 58988)

> Dtrain=bind_rows(CC1train, CC0[train0[1:1200],])  # bind the rows from two data together

> dim(Dtrain)

[1] 1592   31

> Dtrain=arrange(Dtrain, Time)  # re-arrange rows according to ascending order of Time

> write.csv(Dtrain, row.names=F, "creditCardTrain.csv")

> Dtest=bind_rows(CC1test, CC0[train0[1200:58988],])

> dim(Dtest)

[1] 57889    31

> Dtest=arrange(Dtest, Time)

> write.csv(Dtest, row.names=F, "creditCardTest.csv")

> rm(CC, CC0, CC1, CC1test, CC1train, Dtest, Dtrain, train0, train1) # remove those objects

Your analysis should be based on creditCardTrain .csv. creditCardTest .csv represents the true reality, and should be used only to test the performance of your models.

1. Carry out some exploratory data analysis first. You may like to address the issues such as

• are there any missing values and outliers?            [5 marks]

• should you apply any transformations to any variables, for example, log(Amount + 1)?           [10 marks]

• is Time relevant to detecting frauds?           [5 marks]

2. Suppose that the credit card company charges 2% fees for each transaction (deducted from the payment to payee).

(a) Estimate the expected potential loss of a fraudulent transaction.                                   [5 marks]

(b) Estimate the expected profit from a genuine transaction.                                             [5 marks]

(c) Let α denote the probability that a transaction is fraud. What is the minimum value of α to declare ‘Fraud’ in order to ensure that the expected profit from a single transaction is non-negative? [5 marks]

A simple illustration on how a credit card works: Suppose you purchase an item from a shop for £100 payed out of your credit card, the credit card company will pay £98 to the shop at the time.  By the end of the month, you pay back ££100 to the credit card company. So the company make a profit of £2. But if the purchase was not made by you (i.e. a fraud), you will not pay anything to the credit card company. The company will make a loss of £98.

3. Let the profit matrix be

           non-Fraud      Fraud

No                  B             −C

Yes               −1               0

where C and B  are calculated, respectively, in 2(a) and 2(b) tomer’s unhappiness when a genuine transaction is denied.

(a) Construct a decision tree for detecting frauds.

(b) Find the value of the cutting-of probability, denoted by α(^), which maximizes the expected profit. [10 marks]

(c) Test the performance of your decision tree on the testing data set, with the cutting-of probability 0.5 andα(^) respectively. Now you should calculate the true profits or losses according to the real amount of each transaction in the testing data sets.                                       [10 marks]

(d) Construct a logistic regression model for detecting frauds. You may use the same predictor selected in the tree model above.         [10 marks]

(e) Plot the ROC curves with the testing data for both the tree and the logistic regression classifiers constructed above, and compare them using the ‘area under curve’ .                               [15 marks]

4. In your opinion, what are the pros and cons of the above analysis? Do you have any suggestions for further improvement?                       [10 marks]

Note. The strategy to build classifiers using a subset with a much higher positive rate was merged after some initial and less successful attempts. This learning process also re丑ects one important principle of data analytics:

Iteration is the law of learning!