I am working on a problem which looks like this:
The major issue that I am facing is that Output Variables are not totally independent of each other and there is no relation that can be established between them. That is, there is a dependence but not due to the causality (one value being high doesn't imply that the other will be high too but the chances of other being higher will improve)
An Example would be:
v - Number of Ad Impressions
x - Number of Ad Clicks
y - Number of Conversions
z - Revenue
Now, for an Ad to be clicked, it has to first appear on a search, so Click is somewhat dependent on Impression.
Again, for an Ad to be Converted, it has to be first clicked, so again Conversion is somewhat dependent on Click.
So running 4 instances of the problem predicting each of the output variables doesn't make sense to me. Infact there should be some way to predict all 4 together taking care of their implicit dependencies.
But as you can see, there won't be a direct relation, infact there would be a probability that is involved but which can't be worked out manually.
Plus the output variables are not Categorical but are in fact Discrete and Continuous.
Any inputs on how to go about solving this problem. Also guide me to existing implementations for the same and which toolkit to use to quickly implement the solution.
Just a random guess - I think this problem can be targeted by Bayesian Networks. What do you think ?