diff --git a/ObsidianNotes/.obsidian/workspace.json b/ObsidianNotes/.obsidian/workspace.json index 063dc0d..83ea178 100644 --- a/ObsidianNotes/.obsidian/workspace.json +++ b/ObsidianNotes/.obsidian/workspace.json @@ -14,7 +14,7 @@ "type": "markdown", "state": { "file": "elemlds lecture 8.md", - "mode": "source", + "mode": "preview", "source": false }, "icon": "lucide-file", @@ -201,8 +201,8 @@ }, "active": "d74c0c464422592b", "lastOpenFiles": [ - "elemlds lecture 8.md", "elemlds lecture 9.md", + "elemlds lecture 8.md", "Elements of Machine Learning and Data Science.md", "Welcome.md" ] diff --git a/ObsidianNotes/elemlds lecture 9.md b/ObsidianNotes/elemlds lecture 9.md index 0cccec6..afc5ca7 100644 --- a/ObsidianNotes/elemlds lecture 9.md +++ b/ObsidianNotes/elemlds lecture 9.md @@ -5,3 +5,18 @@ Goal: predict output class $\mathcal{C}$ from measurements $\text{x}$ by minimiz >$$p(X,Y)=\frac{p(X|Y)p(Y)}{p(X)}$$ +--- + +$posterior = \frac{likelihood \cdot prior}{normalization factor}$ + + +==NOTE: Learn Normal/Gaussian Distribution by heart!== +univariate: +$$ +\mathcal{N} (x|\mu, \sigma^2) = \frac{1}{\sqrt{2\pi}\sigma}\exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right) +$$ +multivariate: +$$ +\mathcal{N}(\text{x}|\mu, \Sigma) = \frac{1}{(2\pi)^{D/2}|\Sigma|^{1/2}}\exp\left(-\frac{1}{2} (\text{x}-\mu)^\top \Sigma^{-1}(\text{x}-\mu) \right) +$$ +