Machine learning input relationships After learning about a few machine-learning models (NN, SVM, decision trees), I was wondering if these models are able to find inherent relationships when learning. For example, if I feed it two inputs A and B, but it is really A - B or the percent change from A to B that determines the output (but this relationship is unknown to me), would these models be able to pick up that relationship from just the A and B inputs? What about more complicated relationships?
 A: If I understand correctly, you are asking that; given there is a true underlying model, e.g. y = f(A,B), will any of the above learners discover and return the mathematical form of that relationship. The answer is no. Although, something like a neural network is sometimes called a universal function approximator, it is often discarded in favor of a more explainable model, like a linear model. In that case, the mathematical form is known.
For what you are describing, the use of evolutionary algorithms (e.g. genetic programming) are often used to find mathematical relationships between input predictors and output response. 
If you are only asking if they can find some complex hidden relationships, without necessarily revealing the mathematical form of the model, then I agree with bayerj-- Yes.
A: Yes, they can.
All these models have the so called "universal approximation" property: they can approximate any function up to arbitrary accuracy. Yet, that statement is not about finding the parameters, i.e. optimization. That is a problem which is left to the user.
A: I don't know if the models you described above can find this relationship. For regression purposes when you want to learn the regression function maybe you can do this with Bayesian machine learning using Gaussian Processes. These can be used for regression - classification now matter what form has the true regression function. You can check the monograph of C. E Rasmussen and C. K. I Williams which is available for free online
