From: ted.dunning@gmail.com   
      
   You are starting in pretty much the standard place, but your first step   
   from there is not quite what is done in a real recommendation system.   
      
   The thing you are trying to predict is whether somebody would buy   
   something, not whether they have it or would want it.  This sounds like   
   a trivial difference, but it has massive implications.   
      
   First of all, purchase is observable, preference is generally not.   
   Secondly, you don't really care if you are predicting future purchase   
   from past purchases or the phase of the moon.  Any feature that works   
   is good (to quote the Butch Cassidy movie, there are no rules in a   
   knife fight).   
      
   Thus, you are trying to predict proclivity to purchase given   
   *everything* you know about the person and *everything* you know about   
   people in general.  Moreover, in any given moment, the person is fixed   
   and the items to be recommended are variable.  This limits the problem   
   somewhat.   
      
   >From there, the decision comes down to a simple financial decision of   
   what item has a higher expected profit.  Advanced systems of this sort   
   also put a value on knowledge so they might recommend something as a   
   probe so that they can learn about the behavior of your kind of people   
   with that kind of item.   
      
   In my own work on the subject (at Musicmatch where we tripled revenues   
   by optimizing the sales process and recommendations), I found it best   
   to take a radically different approach.  The difference was that we   
   took the point of view that what matters is not the instantaneous   
   expected return, but rather the overall life cycle revenues (profits).   
   For example, you might find that if you offer a cardboard cutout of a   
   Mercedes for $1000 that you get lots of short term sales because on   
   your web-site nobody can tell that it isn't a real car.  The long-term   
   view of the net present value of this offer would, however, indicate   
   that it is a complete disaster due to returns, customers never   
   returning and the cost of litigation.  The life-cycle view accounts for   
   these effects.   
      
   The overall problem is extremely difficult, especially when you have   
   low data rates and limited manpower for analysis and optimization.   
   There are effective solutions, however.   
      
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