Definition

Prediction in statistical learning

A prediction problem in statistical learning occurs when there are a significant number of observations and their corresponding outcomes, and the goal is to predict outcomes for a new set of observations where they are unavailable. Let XX be the set of all input variables and YY be the set of corresponding outcomes. If f^\hat{f} is the estimate of the function ff that maps XX to YY, and Y^\hat{Y} is the resulting prediction of YY, assuming the error term averages to zero (ϵˉ=0\bar{\epsilon}=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 2026-06-13

Tags

Data Science