Machine learning （6-Logistic Regression）

1、Classification

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• However,
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2、Hypothesis Representation

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• Python code:

import numpy as np
def sigmoid(z):
 return 1 / (1 + np.exp(-z))

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• ℎ_𝜃 (𝑥) = 𝑃(𝑦 = 1|𝑥; 𝜃)
• ℎ_𝜃 (𝑥) = 0.7，表示有 70%的 几率𝑦为正向类，相应地𝑦为负向类的几率为 1-0.7=0.3

3、Decision Boundary

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• We can use very complex models to adapt to the decision boundary of very complex shapes

4、Cost Function

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• Python code：

import numpy as np
def cost(theta, X, y):
 theta = np.matrix(theta)
 X = np.matrix(X)
 y = np.matrix(y)
 first = np.multiply(-y, np.log(sigmoid(X* theta.T)))
 second = np.multiply((1 - y), np.log(1 - sigmoid(X* theta.T)))
 return np.sum(first - second) / (len(X))

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5、Simplified Cost Function and Gradient Descent

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6、Advanced Optimization

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7、Multi-class Classification_ One-vs-all

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