elemlds 9 update

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"
   ]

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:
+$$
+\mathcal{N}(\text{x}|\mu, \Sigma) = \frac{1}{(2\pi)^{D/2}|\Sigma|^{1/2}}\exp\left(-\frac{1}{2} (\text{x}-\mu)^\top \Sigma^{-1}(\text{x}-\mu) \right)
+$$
+