Bayesian Network & Anomaly Detection

Transcription

1 Study Unit 6 Bayesian Network & Anomaly Detection ANL 309 Business Analytics Applications

2 Introduction Supervised and unsupervised methods in fraud detection Methods of Bayesian Network and Anomaly Detection

3 Business Analytical Methods for Fraud Detection Business analytical methods for fraud detection may be categorised as Supervised Unsupervised

4 Supervised Methods for Fraud Detection Samples of both fraudulent and non-fraudulent records are used to construct models which allow one to assign new observations into one of the two classes: fraud or non-fraud. Examples of Supervised Methods: - Neural network - Bayesian network

5 Unsupervised Methods for Fraud Detection Unsupervised methods are applied if there are no initial set of fraudulent observations. Unsupervised techniques combine both profiling of customers and detection of outliers. An example of unsupervised methods would be Anomaly Detection.

6 Bayesian Network A business may be interested in finding out the probability of fraud given the evidence. Profiling the historic (training) data will only give the probability of the evidence if it is fraudulent. A Bayesian approach allows the use of these prior probabilities to compute the desired posterior probabilities.

7 Bayesian Network 2 Let F be an event that a transaction is fraudulent. The probability of an event being fraudulent given the evidence is denoted by P(F\Evidence) P(F\Evidence) is calculated as follows: Where P(Evidence)=P(Evidence\F)*P(F)+P(Evidence\Not F)*P(Not F)

8 Bayesian Network 3 Bayesian Network (or a belief network) A probabilistic graphical model representing a set of variables and their probabilistic independencies. For example, a Bayesian Network could represent the probabilistic relationships between a fraud and the symptoms to detect a fraud. Given the symptoms, the network can be used to compute the probabilities of a fraud.

9 Bayesian Network 4 Bayesian Networks are directed acyclic graphs. A directed graph or digraph is an ordered pair (V,A) with: V: a set whose elements are called vertices or nodes A: a set of ordered pairs of vertices, called arcs, directed edges or arrows

10 What is a Directed Cyclic Graph? A directed cyclic graph is a directed version of a cycle graph, with all the edges being oriented in the same direction.

11 What is a Directed Acyclic Graph? A directed acyclic graph (DAG) is a directed graph that do not have any cycle. For any vertex (v), there is no non-empty directed d path that t starts t and ends on v. In other words, a DAG flows in a single direction

12 Child and Parent If there is an arc from node A to node B, A is called a parent of B, and B is a child of A.

13 Bayesian Network 5

14 Anomaly Detection Anomaly Detection ti is an unsupervised method which h identifies outliers and unusual cases in the data.

15 Advantages of Anomaly Detection An Anomaly Detection models stores information on normal behaviour, so outliers (such as fraud) can be identified even if they do not conform to any known pattern. It does not require a training dataset with known cases of fraud. It can handle a large number of fields.

16 Anomaly Detection: An Illustration Suppose the algorithm identifies three clusters. Records A, B and C which fall far below the centre of any one cluster, are flagged.