diff --git a/iml/chapters/various.tex b/iml/chapters/various.tex index b347c00..e804b08 100644 --- a/iml/chapters/various.tex +++ b/iml/chapters/various.tex @@ -1,9 +1,9 @@ \section*{Various} $$\nabla_x x^\top A = A \quad \nabla_x a^\top x = \nabla_x x^\top a = a$$ -$$\nabla_x b^\top A x = A^\top b \quad \nabla_x x^\top x = 2x \quad \nabla_x x^\top A x = (A + A^\top)x$$\\[-20pt] +$$\nabla_x b^\top A x = A^\top b \quad \nabla_x x^\top x = 2x$$\\[-20pt] $$\nabla_w || y-Xw||_2^2 = 2X^\top(Xw-y)$$ -$$(A^{-1})' = -A^{-1} A' A^{-1}$$ +$$(A^{-1})' = -A^{-1} A' A^{-1} \quad \nabla_x x^\top A x = (A + A^\top)x$$ \textbf{Bayes Theorem}: $p(y \; | \; x) = \frac{1}{p(x)} \underbrace{p(y) \cdot p(x \; | \; y)}_{p(x,y)}$