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update derivatives section to prevent overflow
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Signed-off-by: Thomas Gassmann <[email protected]>
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thomasgassmann committed Jul 8, 2024
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4 changes: 2 additions & 2 deletions iml/chapters/various.tex
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\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}: $p(y \; | \; x) = \frac{1}{p(x)} \underbrace{p(y) \cdot p(x \; | \; y)}_{p(x,y)}$

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