6.16 Fraud detection. To prevent fraud, a credit-card company decides to contact Professor Villebanque and provides him
Question:
6.16 Fraud detection. To prevent fraud, a credit-card company decides to contact Professor Villebanque and provides him with a random list of several thousand fraudulent and non-fraudulent events. There are many dierent types of events, e.g., transactions of various amounts, changes of address or card-holder information, or requests for a new card. Professor Villebanque decides to use SVMs with an appropriate kernel to help predict fraudulent events accurately.
It is dicult for Professor Villebanque to dene relevant features for such a diverse set of events. However, the risk department of his company has created a complicated method to estimate a probability P[U] for any event U. Thus, Professor Villebanque decides to make use of that information and comes up with the following kernel dened over all pairs of events (U; V ):
K(U; V ) = P[U ^ V ] ???? P[U] P[V ]: (6.31)
Help Professor Villebanque show that his kernel is positive denite symmetric.
Step by Step Answer:
Foundations Of Machine Learning
ISBN: 9780262351362
2nd Edition
Authors: Mehryar Mohri, Afshin Rostamizadeh