data_mining:logistic_regression

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data_mining:logistic_regression [2014/07/20 16:49] – [Adressing Overfitting] phreazerdata_mining:logistic_regression [2018/05/10 17:48] (current) – phreazer
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 Z.B. aus 3-Klassenproblem 3 binäre Probleme erzeugen. $h_\theta(x)^{(i)} = P(y=i|x;\theta); i=1,2,3$ Z.B. aus 3-Klassenproblem 3 binäre Probleme erzeugen. $h_\theta(x)^{(i)} = P(y=i|x;\theta); i=1,2,3$
  
-Dann wähle Klasse i, die $max_i h_\theta^{(i)}(x)$+Dann wähle Klasse i, die $\max_i h_\theta^{(i)}(x)$
  
 ===== Adressing Overfitting ===== ===== Adressing Overfitting =====
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 $min \dots + \lambda \sum_{i=1}^n \theta_j^2$ $min \dots + \lambda \sum_{i=1}^n \theta_j^2$
  
 +=== Gradient descent (Linear Regression) ===
 +
 +$\dots + \lambda / m \theta_j$
 +
 +$\theta_j := \theta_j (1-\alpha \frac{\lambda}{m}) - \alpha \frac{1}{m} \sum^m_{i=1} (h_\theta(x^{(i)} - y^{(i)}) x_j^{(i)}$
 +
 +
 +=== Normalengleichung (Linear Regression) ===
 +$$(x^T X + \lambda 
 +\begin{bmatrix}
 +0 & \dots & \dots & 0 \\
 +\vdots & 1 & 0 & \vdots \\
 +\vdots & 0 & \ddots & 0 \\
 +0 & \dots & 0 & 1
 +\end{bmatrix})^{-1} X^T y$$
 +
 +=== Gradient descent (Logistic Regression) ===
 +
 +Unterscheide $\theta_0$ und $\theta_j$!
 +
 +Für $\theta_j$: $\dots + \frac{\lambda}{m} \theta_j$
  • data_mining/logistic_regression.1405867770.txt.gz
  • Last modified: 2014/07/20 16:49
  • by phreazer