Quote:
Originally Posted by magdon
This is a good question. The general conclusion you made is correct, that more or less the same problem with different lingo is addressed in function approximation arising from the statistics community and supervised learning arising in the learning community. But if you read a statistics book on function approximation, it will look very different from the text related to this forum. So while the problem is the same, (inputoutput examples to learn a funcction f), the approaches in these two fields are different.
Largely, the difference is in the assumptions made and the nature of the results. In the statistics approach one usually makes distributional assumptions on the nature of the data and then derives how a particular model like the linear model will behave. Function approximation in statistics typically only discusses regression problems. In learning, we make very mild assumptions and obtain different types of results, and we have a particular focus on classification.
Section 1.2 gives a short discussion of different types of learning that may be helpful.

True that statistics often makes distributional assumptions. But what about the field of nonparametric statistics, which makes little to no assumptions about distributions? Many interesting techniques there like resampling and the jackknife.