吴恩达机器学习笔记（七）--Logistic回归

吴恩达机器学习笔记（七）–Logistic回归

学习基于：吴恩达机器学习

1. Classification

• The classification problem is just like the regression problem, except that the values we now want to predict take on only a small number of discrete values.
• Linear regression doesn’t work well here because classification is not actually a linear function.

classification problems:

E-mail: spam / Not spam ?

Online transactions: Fraudulent or not ?

Tumor: Malignant / Benign ?

2. Hypothesis Representation

We will change the form for our hypotheses ??(x) to satisfy 0≤ ??(x)≤1. These are Sigmoid Function, also called Logistic function.

• $h_{\theta }(x)=g({\theta }^{T}x)$
• $z={\theta }^{T}x$
• $g(z)=\frac{1}{1-e^z}$

The following image shows us what the sigmoid function looks like:

The function g(z), shown here, maps any real number to the (0, 1) interval, making it useful for transforming an arbitrary-valued function into a function better suited for classification.

??(x) will give us the probability that our output is 1. For example, ??(x)=0.7 gives us a probability of 70% that our output is 1.