Logistic Regression
-NOTES, NEEDS FINISHING-
Basic classification algorithm used for prediction of the probability of occurrence of an event by fitting data to a logit function logistic curve.
Hypothesis Representation
In logistic regression, we want the hypothesis to be $$0 \le h_\theta(x) \le 1$$
For this, we use the Sigmoid or Logistic Function
$$\begin{eqnarray} g(z) &=& { \frac{1}{1 + e^{-z}} } \\ h_\theta(x) &=& g(\theta^T x) \\ h_\theta(x) &=& { \frac{1}{1 + e^{-\theta^T x}} } \end{eqnarray}$$
Plot of \(g(z)\)
In Octave it looks something like the following
