Let's say I have an n x p dataset. For each n, I have the response, 'y', and p - 1 features associated with it. What is the best way to determine the values of the features that will maximize 'y'? The only way I can think of is to build a model, regression or otherwise, and then perform multivariable optimization on the resulting equation. Is there a better way to do this?
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What you describe appears "reasonable" as a first approach but you need to need to be careful on how will you generalize your findings. Check the responses in the following link concerning Feature selection and Cross-Validation, I think you'll find them quite helpful: http://stats.stackexchange.com/questions/27750/feature-selection-and-cross-validation/ – usεr11852 Apr 17 '14 at 01:29