Please do it in python please.

Every year, credit card companies lose millions of dollars due to frauds resulting from lost or stolen cards. Recently, the financial industry has turned to AI for solutions to the fraud detection problem. Intuitively, credit card holders tend to make purchases following a certain pattern. A fraud is likely to happen when this pattern is broken. In this assignment you will implement a simple fraud detection system in 3 steps. First, you will implement the variable elimination algorithm. Second, you will define your fraud detection system as a Bayesian network and compute the likelihood of a fraud in different situations. Third, you will extend your Bayesian network to a decision network which will be used to decide when a transaction should be blocked. Computations in your Bayesian network and your decision network should be done with your implementation of the variable elimination algorithm. However, if you are not able to complete your implementation of variable elimination, you can also do the computations by hand since they are simple.

Part 1 (1 point)

Implement the variable elimination algorithm by coding the following 4 functions in the programming language of your choice.

restrictedFactor = restrict (factor, variable, value): function that restricts a variable to some value in a given factor.

productFactor = multiply (factor1, factor2): function that multiplies two factors.

resultFactor = sumout (factor, variable): function that sums out a variable in a given factor.

resultFactor = inference (factorList, queryVariables, orderedListOfHiddenVariables, evidence List): function that computes P r(queryVariables|evidenceList) by variable elimination. This function should restrict the factors in factorList according to the evidence in evidenceList. Next, it should sumout the hidden variables from the product of the factors in factorList. The variables should be summed out in the order given in orderedListOfHiddenVariables. Finally, the answer should be normalized to make sure that the probability distribution sums up to 1.

Tip: factors are multi-dimensional arrays, so you may want to use this data-structure, but feel free to use a different data-structure.

Tip: test each function individually using simple examples. If you wait till the end to test your entire program it will be much harder to debug.

Part 2 (2 points)

Suppose you are working for a financial institution and you are asked to implement a fraud detection system. You plan to use the following information:

When the card holder is travelling abroad, fraudulent transactions are more likely since tourists are prime targets for thieves. More precisely, 1% of transactions are fraudulent when the card holder is travelling, whereas only 0.2% of the transactions are fraudulent when she is not travelling. On average, 5% of all transactions happen while the card holder is travelling. If a transaction is fraudulent, then the likelihood of a foreign purchase increases, unless the card holder happens to be travelling. More precisely, when the card holder is not travelling, 10% of the fraudulent transactions are foreign purchases whereas only 1% of the legitimate transactions are foreign purchases. On the other hand, when the card holder is travelling, then 90% of the transactions are foreign purchases regardless of the legitimacy of the transactions.

Purchases made over the internet are more likely to be fraudulent. This is especially true for card holders who dont own any computer. Currently, 60% of the population owns a computer and for those card holders, 1% of their legitimate transactions are done over the internet, however this percentage increases to 2% for fraudulent transactions. For those who dont own any computer, a mere 0.1% of their legitimate transactions is done over the internet, but that number increases to 1.1% for fraudulent transactions. Unfortunately, the credit card company doesnt know whether a card holder owns a computer, however it can usually guess by verifying whether any of the recent transactions involve the purchase of computer related accessories. In any given week, 10% of those who own a computer purchase with their credit card at least one computer related item as opposed to just 0.1% of those who dont own any computer.

Construct a Bayes Network that your fraud detection system can use to identify fraudulent transactions.

Show the graph defining the network and the Conditional Probability Tables associated with each node in the graph. This network should encode the information stated above. Your network should contain exactly six nodes, corresponding to the following binary random variables:

OC card holder owns a computer. Fraud current transaction is fraudulent. Trav card holder is currently travelling. FP current transaction is a foreign purchase. IP current purchase is an internet purchase. CRP a computer related purchase was made in the past week.

The arcs defining your Bayes Network should accurately capture the probabilistic dependencies between these variables.

What is the prior probability (i.e., before we search for previous computer related purchases and before we verify whether it is a foreign and/or an internet purchase) that the current transaction is a fraud? What is the probability that the current transaction is a fraud once we have verified that it is a foreign transaction, but not an internet purchase and that the card holder purchased computer related accessories in the past week?

Indicate what queries (i.e., P r(variables|evidence)) you used to compute those probabilities. Whether you answer the queries by hand or using the code you wrote for Part 1, provide a printout of the factors computed at each step of variable elimination. Use the following variable ordering when summing out variables in variable elimination: Trav, FP, Fraud, IP, OC, CRP. Note that you can answer the questions correctly by doing the computations by hand and then use the functions created in part 1 to test your program.

After computing those probabilities, the fraud detection system raises a flag and recommends that the card holder be called to confirm the transaction. An agent calls the home of the card holder, but she is not home. Her spouse confirms that she is currently out of town on a business trip. How does the probability of a fraud change, based on this new piece of information?

Suppose you are not a very honest employee and you just stole a credit card. You know that the fraud detection system uses the Bayes net designed earlier but you still want to make an important purchase over the internet. What can you do prior to your internet purchase to reduce the risk that the transaction will be rejected as a possible fraud? Describe the action taken and indicate by how much the probability of a fraud gets reduced.