diff --git a/iml/chapters/generative-modeling.tex b/iml/chapters/generative-modeling.tex index de08eaa..8f860b7 100644 --- a/iml/chapters/generative-modeling.tex +++ b/iml/chapters/generative-modeling.tex @@ -53,4 +53,4 @@ \subsection*{Generative vs. Discriminative} \textbf{Generative models}: -$p(x,y)$, can be more powerful (dectect outliers, missing values) if assumptions are met, are typically less robust against outliers +$p(x,y)$, can be more powerful (detect outliers, missing values) if assumptions are met, are typically less robust against outliers diff --git a/iml/chapters/various.tex b/iml/chapters/various.tex index e3ff887..3700061 100644 --- a/iml/chapters/various.tex +++ b/iml/chapters/various.tex @@ -50,5 +50,5 @@ \section*{Various} $M \in \mathbb{R}^{n\times n}$ PSD $\Leftrightarrow \forall x \in \mathbb{R}^n: x^\top Mx \geq 0 \\ \Leftrightarrow$ all principal minors of $M$ have non-negative determinant $\Leftrightarrow \lambda \geq 0 \ \forall \lambda\in\sigma(M)$ -\textbf{CLT} For $X_i$ iid with $m = \E[X_1]$ and $\Var[X_1] = \sigma^2$: $\mathbb{P}\left[\frac{\sum_{i=1}^n X_i - n m}{\sqrt{\sigma^2 n}} \leq a\right] \xrightarrow[n \to \infty]{} \Phi(a)$. -\textbf{KL Divergence} $D_{KL}(P||Q) = \mathbb{E}_p[\log(\frac{p(x)}{q(x)})]$, 0 iff $P = Q$, always non-negative \ No newline at end of file +\textbf{CLT} For $X_i$ iid with $m = \E[X_1]$ and $\text{Var}(X_1) = \sigma^2$: $\mathbb{P}\left[\frac{\sum_{i=1}^n X_i - n m}{\sqrt{\sigma^2 n}} \leq a\right] \xrightarrow[n \to \infty]{} \Phi(a)$. +\textbf{KL Divergence} $D_{KL}(P||Q) = \mathbb{E}_p[\log(\frac{p(x)}{q(x)})]$, 0 iff $P = Q$, always non-negative