data_mining:regression

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data_mining:regression [2014/07/13 03:11] – [Learning rate $\alpha$] phreazerdata_mining:regression [2014/07/13 03:37] – [Normalengleichungen] phreazer
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 $\theta_j := \theta_j - alpha \frac{\partial}{\partial\theta_j} J(\theta)$ $\theta_j := \theta_j - alpha \frac{\partial}{\partial\theta_j} J(\theta)$
 +
 +
 +==== Normalengleichungen ==== 
 +
 +  * Feature-/Designmatrix X (Dim: m x (n+1))
 +  * Vector y (Dim: m)
 +
 +$\theta = (X^TX)^{-1}X^Ty$
 +
 +  * Feature scaling nicht notwendig.
 +
 +Was wenn $X^TX$ singulär (nicht invertierbar)?
 +
 +(pinv in Octave)
 +
 +**Gründe für Singularität:**
 +  * Redundante Features (lineare Abhängigkeit)
 +  * Zu viele Features (z.B. $m <= n$)
 +    * Lösung: Features weglassen oder regularisieren
 +
 +**Wann was benutzten?**
 +
 +  * m training tupel, n features
 +  * GD funktioniert bei großem n (> 1000) gut, Normalengleichung muss (n x n) Matrix invertieren, liegt ungefähr in $O(n^3)$.
  
 ===== Gradient Descent Improvements ===== ===== Gradient Descent Improvements =====
  • data_mining/regression.txt
  • Last modified: 2019/02/10 17:14
  • by phreazer