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elemlds 9 update

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Tom Zuidberg
2026-02-10 14:40:49 +01:00
parent c394ee2cce
commit 4707650c58
2 changed files with 17 additions and 2 deletions
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4
ObsidianNotes/.obsidian/workspace.json vendored
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@@ -14,7 +14,7 @@
"type": "markdown", "type": "markdown",
"state": { "state": {
"file": "elemlds lecture 8.md", "file": "elemlds lecture 8.md",
"mode": "source", "mode": "preview",
"source": false "source": false
}, },
"icon": "lucide-file", "icon": "lucide-file",
@@ -201,8 +201,8 @@
}, },
"active": "d74c0c464422592b", "active": "d74c0c464422592b",
"lastOpenFiles": [ "lastOpenFiles": [
"elemlds lecture 8.md",
"elemlds lecture 9.md", "elemlds lecture 9.md",
"elemlds lecture 8.md",
"Elements of Machine Learning and Data Science.md", "Elements of Machine Learning and Data Science.md",
"Welcome.md" "Welcome.md"
] ]

15
ObsidianNotes/elemlds lecture 9.md
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@@ -5,3 +5,18 @@ Goal: predict output class $\mathcal{C}$ from measurements $\text{x}$ by minimiz
>$$p(X,Y)=\frac{p(X|Y)p(Y)}{p(X)}$$ >$$p(X,Y)=\frac{p(X|Y)p(Y)}{p(X)}$$
---
$posterior = \frac{likelihood \cdot prior}{normalization factor}$
==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:
$$
\mathcal{N}(\text{x}|\mu, \Sigma) = \frac{1}{(2\pi)^{D/2}|\Sigma|^{1/2}}\exp\left(-\frac{1}{2} (\text{x}-\mu)^\top \Sigma^{-1}(\text{x}-\mu) \right)
$$