代码：
# Machine Learning Online Class - Exercise 2: Logistic Regression
import numpy as np
import matplotlib.pyplot as plt
import scipy.optimize as op
def sigmoid(x):
return 1 / (1 + np.exp(-x))
def plotData(X, y):
index0 = list()
index1 = list()
j = 0
for i in y:
if i == 0:
index0.append(j)
else:
index1.append(j)
j = j + 1
plt.scatter(X[index0, 0], X[index0, 1], marker='o')
plt.scatter(X[index1, 0], X[index1, 1], marker='+')
plt.xlabel('Exam 1 score')
plt.ylabel('Exam 2 score')
plt.legend(['Admitted', 'Not admitted'], loc='upper right')
#plt.show()
def costFunction(initial_theta, X, y, myLambda):
m = y.shape[0]
#grad = np.zeros((initial_theta.shape))
J = np.sum(np.dot((-1*y).T, np.log(sigmoid(np.dot(X, initial_theta))))
- np.dot((1-y).T, np.log(1 - sigmoid(np.dot(X, initial_theta)))))/m
#grad = np.dot(X.T, sigmoid(np.dot(X, initial_theta)) - y)/m
return J # , grad
def gradient(initial_theta, X, y, myLambda):
m, n = np.shape(X)
initial_theta = initial_theta.reshape((n, 1))
# print(initial_theta.shape)
#grad = np.zeros((initial_theta.shape))
grad = np.dot(X.T, sigmoid(np.dot(X, initial_theta)) - y)/m
#grad = ((X.T).dot(sigmoid(np.dot(X, initial_theta)) - y)) / m
return grad.flatten()
def plotDecisionBoundary(theta, X, y):
figure = plotData(X[:, 1:], y)
m, n = X.shape
# Only need 2 points to define a line, so choose two endpoints
if n <= 3:
point1 = np.min(X[:, 1])
point2 = np.max(X[:, 1])
point = np.array([point1, point2])
plot_y = -1*(theta[0] + theta[1]*point)/theta[2]
plt.plot(point, plot_y, '-')
plt.legend(['Admitted', 'Not admitted', 'Boundary'], loc='lower left')
plt.show()
return 0
def predict(theta, X):
m, n = X.shape
p = np.zeros((m, 1))
k = np.where(sigmoid(X.dot(theta)) >= 0.5)
p[k] = 1
return p
if __name__ == '__main__':
# Load Data
data = np.loadtxt('ex2data1.txt', delimiter=',')
X = data[:, 0:2]
y = data[:, 2].astype(int)
y = np.reshape(y, (y.shape[0], 1)) # 把y转换成mx1的列向量
# ==================== Part 1: Plotting ====================
print('Plotting data with + indicating (y = 1) examples \
and o indicating (y = 0) examples')
plotData(X, y)
print("="*40)
# ============ Part 2: Compute Cost and Gradient ============
# Setup the data matrix appropriately, and add ones for the intercept term
(m, n) = X.shape
X = np.column_stack((np.ones((m, 1)), X))
(m, n) = X.shape
initial_theta = np.zeros((n, 1)) # nitialize fitting parameters
myLambda = 0
# Compute and display initial cost and gradient
cost = costFunction(initial_theta, X, y, myLambda)
grad = gradient(initial_theta, X, y, myLambda)
print('Cost at initial theta (zeros):', cost)
print('Expected cost (approx): 0.693\n')
print('Gradient at initial theta (zeros): ')
print(grad)
print('Expected gradients (approx):\n -0.1000\n -12.0092\n -11.2628\n')
# Compute and display cost and gradient with non-zero theta
test_theta = np.array([[-24], [0.2], [0.2]])
cost = costFunction(test_theta, X, y, myLambda)
grad = gradient(initial_theta, X, y, myLambda)
print('Cost at initial theta :', cost)
print('Expected cost (approx): 0.218\n')
print('Gradient at initial theta : ')
print(grad)
print('Expected gradients (approx):\n 0.043\n 2.566\n 2.647\n')
print("="*40)
# ============= Part 3: Optimizing using fminunc =============
# In this exercise, you will use a built-in function (fminunc) to find the
# optimal parameters theta.
myLambda = 1
# Result = op.minimize(fun=costFunction, x0=initial_theta, args=(X, y, myLambda), method='TNC', jac=gradient)
Result = op.minimize(fun=costFunction, x0=initial_theta,
args=(X, y, myLambda), method='TNC', jac=gradient)
#Result = op.fmin_tnc(func=costFunction,x0=initial_theta,args=(X,y))
# Result = op.fmin_bfgs(f=costFunction,x0=initial_theta,fprime=gradient(X,y，1),gtol=1e-5,\disp=1)
theta = Result.x
cost = Result.fun
print('Cost at theta found by fminunc:', cost)
print('Expected cost (approx):0.203\n')
print('theta:', theta)
print('Expected theta (approx):[-25.161 0.206 0.201]\n')
plotDecisionBoundary(theta, X, y)
print('='*40)
# ============== Part 4: Predict and Accuracies ==============
sample = np.array([1, 45, 85])
prob = sigmoid(np.dot(sample, theta))
print('For a student with scores 45 and 85, we predict an admission\
probability of ', prob)
print('Expected value: 0.775 +/- 0.002\n\n')
# compute accuracy on our training set
p = predict(theta, X)
accuracy = np.mean(np.double(p == y)) * 100
print('Train Accuracy:', accuracy)
print('Expected accuracy (approx): 89.0')
print('='*40)
运行结果
踩到的坑：
1、经常手误把np.ones() 和 np.zeros() 混淆
2、在处理正则化项的theta时出错：自以为是地把theta第一列全部变成0，在合并向量时检索错误（神奇的是，此时计算Lambda=1的结果正确）
正确的做法是把theta的第一项变为0（theta为（n x 1）的列向量)
原因：对正则化理解不透彻
3、array作为参数传入到定义的函数里时，shape可能会改变。这里遇到的坑是：
initial_theta在设定时是(28,1)，但到了def costFunctionReg_grad()的肚子里面就变成了(28, )，
如果不reshape一下，就会报错：“ValueError: operands could not be broadcast together with shapes (28,118) (28,) ”
这是经常踩到的坑！！！！！