How to model user's buying behavior on Amazon?
How will you validate your algorithm?

Rather than trying to answer the second question, consider that your answer to the first question might need revision...

What methods have you used for validating learning methods throughout your data science class?  First you want to define a specific set of numerical metrics to assess the success or failure of your model. Second, what methods can you use to create a very realistic testing population (more realistic than modeling the population)?  The first hint I will give is that the Amazon Reviews Dataset is very large, so your data is very amendable to this method.  The second hint I will give is that this method is likely the one that you have used in 95% of the supervised learning problems that you have worked on in class...

Hope this helps... I will edit this if need be based on comments added by the OP, but don't want to provide the solution right away in order to elicit some organic thought e.g. since this is a class problem and the Prof is also trying to help you come up with the right solution on your own.