Differences

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--- data_mining:regression [2014/07/13 03:36] – [Normalengleichungen] phreazer
+++ data_mining:regression [2019/02/10 17:14] (current) – [Gradient descent] phreazer
@@ Line 17: / Line 17: @@
 ==== Cost function ====
+$\displaystyle\min_{\theta_0,\theta_1} \sum_{i=1}^m (h_\theta(x^{(i)})-y^{(i)})^2$
-$\text{minimize}_{\theta_0,\theta_1} \sum_{i=1}^m (h_\theta(x^{(i)})-y^{(i)})^2$
 Vereinfachtes Problem:
-$\text{minimize}_{\theta_0,\theta_1} \frac{1}{2*m} \sum_{i=1}^m (h_\theta(x^{(i)})-y^{(i)})^2$
+$\displaystyle\min_{\theta_0,\theta_1} \frac{1}{2*m} \sum_{i=1}^m (h_\theta(x^{(i)})-y^{(i)})^2$
 $h_\theta(x^{(i)}) = \theta_0 +\theta_1x^{(i)}$
-Cost function (Squared error cost function):
+Cost function (Squared error cost function) $J$:
 $J(\theta_0,\theta_1) = \frac{1}{2*m} \sum_{i=1}^m (h_\theta(x^{(i)})-y^{(i)})^2$
-Goal: $\text{minimize}_{\theta_0,\theta_1} J(\theta_0,\theta_1)$
+Goal: $\displaystyle\min_{\theta_0,\theta_1} J(\theta_0,\theta_1)$
 === Functions (example with only $\theta_1$): ===
@@ Line 54: / Line 53: @@
 Wiederholen bis zur Konvergenz:
-$\theta_j := \theta_j - alpha \frac{\partial}{\partial\theta_j} J(\theta_0, \theta_1)$
+$\theta_j := \theta_j - \alpha \frac{\partial}{\partial\theta_j} J(\theta_0, \theta_1)$
 Gleichzeitiges Update (!):
 $$
-tmp0 := \theta_0 - alpha \frac{\partial}{\partial\theta_0} J(\theta_0, \theta_1)\\
+tmp0 := \theta_0 - \alpha \frac{\partial}{\partial\theta_0} J(\theta_0, \theta_1)\\
-tmp1 := \theta_1 - alpha \frac{\partial}{\partial\theta_1} J(\theta_0, \theta_1)\\
+tmp1 := \theta_1 - \alpha \frac{\partial}{\partial\theta_1} J(\theta_0, \theta_1)\\
 \theta_0 := tmp0\\
 \theta_1 := tmp1
@@ Line 120: / Line 119: @@
 **Gründe für Singularität:**
-  * Redundante features (lineare Abhängigkeit)
+  * Redundante Features (lineare Abhängigkeit)
-  * Zu viele Features (z.B. m <= n)
+  * Zu viele Features (z.B. $m <= n$)
     * Lösung: Features weglassen oder regularisieren
 **Wann was benutzten?**