Constructing your features is a nonlinear transform of the raw data. This is what you can do ahead of looking at the data. Construct the best features you can think of. Once you are done there and you still think that you need nonlinear then you can try the generic transforms: polynomial, exponential, etc. or use a more sophisticated method like a neural network or a kernel machine. When using such more complex machines, always ensure that the complexity of the machine is appropriate for the quantity and quality of data you have, and b e prepared to use regularization and validation.
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Originally Posted by GB449
What is the best way to do nonlinear transformation but avoid data snooping? The circle example in lecture 18 was a clear case of data snooping. In practice, what information can we safely use to identify candidate nonlinear transforms? Should we just try a few (e.g. second order, third order polynomials and pick the best (of course, not sequentially & using information from one transform to influence the next candidate, since that will be data affecting the learning process)).
