1. Logistic Regression

• Sigmoid function addresses the classification problem well.
  

• The output of logistic regression is the probability that class is 1 (positive).

2. Decision Boundary

• Above the threshold is positive, while below is negative.
• Threshold does not need to be 0.5.
  • For subjects like brain tumors, it would be safer with lower thresholds, because false positives are safer than false negative.
• If w * x + b >= 0 , then positive. Plotting out w * x+b makes the decision boundary.

3. Cost Function for Logistic Regression

• The squared cost function for logistic regression shows many local minima, which is not ideal for gradient descent.

• The upper branch log function works for y = 1, because the cost decreases exponentially when expected value gets closer to 1.
• Closer to 0, cost goes to infinity.
  
• The opposite for y = 0.