Parametric Methods:

The model based approach that reduces the problem of estimating $f$ to one of estimating a set of parameters. This approach is referred as parametric.

Involves two steps:

1. We make assumption about the functional form distribution of $f$
2. We need a procedure that uses the training data to fit or train the model

NonParametric Methods:

Do not make any explicit assumptions about the functional form of $f$. Suffer from a major dis-advantage.

By not reducing the problem to estimation of parameters a large number of observations are required to get a good estimation of $f$.