AppliedMultiple choice

Setting the gradient of ∥y−Xβ∥2+λ∥β∥2\lVert y - X\beta\rVert^2 + \lambda\lVert\beta\rVert^2 to zero gives which solution?

  1. Aβ=(X⊤X)−1X⊤y−λ\beta = (X^\top X)^{-1}X^\top y - \lambda
  2. Bβ=(X⊤X+λI)−1X⊤y\beta = (X^\top X + \lambda I)^{-1}X^\top y
  3. Cβ=(X⊤X)−1(X⊤y+λ1)\beta = (X^\top X)^{-1}(X^\top y + \lambda\mathbf{1}), adding the penalty to the moments
  4. Dβ=X⊤y/(1+λ)\beta = X^\top y / (1 + \lambda)

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