Concept

Prediction in statistical learning

Prediction problem is defined when we have a significant number of observations and their corresponding outcomes, and we'd like to predict the outcomes for another set of observations where the corresponding outcomes are unavailable. We call the set of all input variables XX, and the corresponding set of all outcomes YY. If we define f^\hat{f} as the estimate of the function ff that we need to estimate to map XX to YY, and we define Y^\hat{Y} as the resulting prediction of YY, and considering the fact that the error term averages to 0, the following holds: Y=f(X)+ϵ,ϵˉ=0,    Y^=f^(X)Y=f(X)+\epsilon, \bar{\epsilon}=0, \implies \hat{Y}=\hat{f}(X)

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Updated 2021-01-24

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Data Science