first week for 10601ML

Author: tmp-coder

10601ML-CMU/CS229-stanford-ML-note/cs229-notes1.pdf

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+import numpy as np
+import matplotlib.pyplot as plt
+
+beta_3_3 = 0.0333
+
+def theta_MLE(theta,n,positive):
+    return (theta ** positive)*((1 - theta) **(n-positive))
+
+
+def theta_MAP(theta,n,positive):
+    return theta_MLE(theta,n,positive) *(theta**2) * (1-theta) ** 2 / beta_3_3
+
+def problem2():
+    theta = np.linspace(0,1,endpoint= False)
+    l_theta = theta_MLE(theta,n=10,positive=6)
+    plt.plot(theta,l_theta,label = 'n=10,positive=6')
+    plt.plot(theta, theta_MLE(theta,5,3),label ='n=5,positive=3')
+    plt.plot(theta,theta_MLE(theta,100,60),label ='n=100,positive = 60')
+    plt.legend()
+    plt.show()
+
+def problem3():
+    theta = np.linspace(0,1,num=100,endpoint=False)
+    y = theta_MAP(theta,10,6)
+    plt.plot(theta,y,label = 'n=10,positive = 3')
+    plt.plot(theta, theta_MAP(theta,5,3),label ='n=5,positive=3')
+    plt.plot(theta,theta_MAP(theta,100,60),label ='n=100,positive = 60')
+    
+    plt.legend()
+    plt.show()
+
+
+if __name__ == "__main__":
+    # problem2()
+    problem3()

10601ML-CMU/CS229-stanford-ML-note/cs229-prob.pdf

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+# problem 2
+
+1. <br>
+
+$$
+\begin{aligned}
+L(\theta) &= \prod \theta^{X_i}(1- \theta) ^{1-X_i}\\
+&= \theta^{\sum X_i}(1-\theta)^{n-\sum X_i}
+\end{aligned}
+$$
+
+2. <br>
+
+    [code](./hw2.py)
+
+    ![Ltheta](img/pb2.png)
+
+3. <br>
+
+$$
+\begin{aligned}
+Ln\ L(\theta) &= ln\ \theta\sum X_i +(n - \sum X_i)ln(1-\theta)\\
+\frac{\partial Ln\ L(\theta)}{\partial \theta} &= \frac{\sum X_i}{\theta} + -1\frac{n - \sum X_i}{1 - \theta}  = 0\\
+\theta& = \frac{\sum X_i}{\theta} = 0.6
+\end{aligned}
+$$
+
+4. <br>
+   
+   ![pb2-3.png](img/pb2-3.png)
+
+# problem 3
+
+
+![pb3-1](img/pb3-1.png)
+