3、Logistic Regression
主要分为三部分：Classification and Representation、Logistic Regression Model、Multiclass Classfication
3.1 Classification and Representation
3.1.1 Classification
Y ∈ {0，1} 0：‘Negative Class’ 1：‘Positive Class’
Classification: hθ(x)可以 >1 or <0
Logistic Regression: 0<= hθ(x) <=1
3.1.2 Hypothesis Representation
hθ(x) = estimated probability that y=1 on input x
3.1.3 Decision Boundary
3.2 Logistic Regression Model
3.2.1 Cost Function
Cost(hθ(x),y) = -log(hθ(x)) if y=1
-log(1-hθ(x)) if y=0
3.2.2 Simplified Cost Function and Gradient Descent
Cost(hθ(x),y) = -ylog(hθ(x)) - (1-y)log(1-hθ(x))
3.3 Multiclass Classification
3.4 Solving the Problem of Overfitting
Overfitting: If we have too many features, the
learning hypoyhesis may fit the training set very well,
but fail to generalize to new examples.
Addressing overfitting:
Options:
1. Reduce number of features.
--Manually select which features to keep.
--Model selection algorithm.
2. Regularization.
--Keep all the features,but reduce magnitude
/values of parameters θj.
--Works well when we have a lo