下面主要提供逻辑回归的代码。
数据下载：数据下载
这是老师布置的作业，现把完整代码附上。
代码如下（python 3.6）：
# -*- encoding: utf-8 -*-
from __future__ import print_function
import numpy as np
import scipy.optimize as op
import matplotlib.pyplot as plt
def plot_data(X, y):
"""This function plots the data points X and y into a new figure.
It plots the data points with red + for the positive examples,
and blue o the negative examples. X is assumed to be a Mx2 matrix.
"""
plt.figure()
# ====================== YOUR CODE HERE ======================
pos = y == 1
neg = y == 0
plt.plot(X[pos, 0], X[pos, 1], 'r+', label="Admitted")
plt.plot(X[neg, 0], X[neg, 1], 'bo', label="Not admitted")
# ============================================================
plt.xlabel("Exam 1 Score")
plt.ylabel("Exam 2 Score")
def plot_decision_boundary(theta, X, y):
"""绘制分类面。"""
plot_data(X[:, 1:], y)
_, d = X.shape
if d <= 3:
plot_x = np.array([np.min(X[:, 1])-2, np.max(X[:, 1])+2])
plot_y = -1.0/theta[2]*(theta[1]*plot_x + theta[0])
plt.plot(plot_x, plot_y, 'm-', label="Decision Boundary")
plt.xlim([30, 100])
plt.ylim([30, 100])
else:
n_grid = 50
u = np.linspace(-1, 1.5, n_grid)
v = np.linspace(-1, 1.5, n_grid)
z = np.zeros((n_grid, n_grid))
for i in range(n_grid):
for j in range(n_grid):
uu, vv = np.array([u[i]]), np.array([v[j]])
z[i, j] = np.dot(map_feature(uu, vv), theta)
z = z.T
CS = plt.contour(u, v, z, lw=2, levels=[0.0], colors=['m'])
CS.collections[0].set_label('Decision boundary')
plt.legend()
def sigmoid(z):
"""Compute sigmoid function"""
z = np.asarray(z)
g = np.zeros_like(z)
# ====================== YOUR CODE HERE ======================
g=1.0/(1.0+np.exp(-z))
# ============================================================
return g
def cost_function(theta, X, y):
"""逻辑回归的代价函数，无正则项。"""
J = 0.0
# ====================== YOUR CODE HERE ======================
m=len(y)
estimation =sigmoid(np.dot(X,theta))
for i in range (X.shape[0]):
J0=-y[i]*np.log(estimation[i])-(1-y[i])*np.log(1-estimation[i])
J=J+J0
J=J/m
# ============================================================
return J
def cost_gradient(theta, X, y):
"""逻辑回归的代价函数的梯度，无正则项。"""
m = 1.0*len(y)
grad = np.zeros_like(theta)
# ====================== YOUR CODE HERE ======================
h_theta = sigmoid(np.dot(X, theta))
grad = np.dot(X.T, h_theta-y)/m
# ============================================================
return grad
def predict(theta, X):
"""Predict whether the label is 0 or 1
using learned logistic regression parameters theta.
"""
m, _ = X.shape
pred = np.zeros((m, 1), dtype=np.bool)
# ====================== YOUR CODE HERE ======================
pred=(sigmoid(np.dot(X,theta)))
for i in range(m):
if pred[i] >= 0.5:
pred[i]=1
else:
pred[i]=0
# ============================================================
return pred
def map_feature(X1, X2, degree=6):
"""Feature mapping function to polynomial features."""
m = len(X1)
assert len(X1) == len(X2)
n = int((degree+2)*(degree+1)/2)
out = np.zeros((m, n))
idx = 0
for i in range(degree+1):
for j in range(i+1):
# print i-j, j, idx
out[:, idx] = np.power(X1, i-j)*np.power(X2, j)
idx += 1
return out
def cost_function_reg(theta, X, y, lmb):
"""逻辑回归的代价函数，有正则项。"""
m = 1.0*len(y)
J = 0
# ====================== YOUR CODE HERE ======================
m=len(y)
estimation =sigmoid(np.dot(X,theta))
for i in range (m):
J0=-y[i]*np.log(estimation[i])-(1-y[i])*np.log(1-estimation[i])
J=J+J0
J=J/m+lmb/(2*m)*np.dot(theta.T,theta)
# ============================================================
return J
def cost_gradient_reg(theta, X, y, lmb):
"""逻辑回归的代价函数的梯度，有正则项。"""
m = 1.0*len(y)
grad = np.zeros_like(theta)
# ====================== YOUR CODE HERE ======================
h_theta = sigmoid(np.dot(X, theta))
grad = np.dot(X.T, h_theta-y)/m
grad=grad-lmb/m*theta[0]
# ============================================================
return grad
def logistic_regression():
"""针对第一组数据建立逻辑回归模型。"""
# 加载数据
data = np.loadtxt("data1.txt", delimiter=",")
X, y = data[:, :2], data[:, 2]
# 可视化数据
plot_data(X, y)
plt.legend()
plt.show()
# 计算代价与梯度
m, _ = X.shape
X = np.hstack((np.ones((m, 1)), X))
print("长度",X,X.shape)
# 初始化参数
theta_initial = np.zeros_like(X[0])#X[0]代表第一行
print("theta的个数",X[0],theta_initial,theta_initial.shape)
# 测试 sigmoid 函数
z = np.array([-10.0, -5.0, 0.0, 5.0, 10.0])
g = sigmoid(z)
print("Value of sigmoid at [-10, -5, 0, 5, 10] are:\n", g)
# 计算并打印初始参数对应的代价与梯度
cost = cost_function(theta_initial, X, y)
grad = cost_gradient(theta_initial, X, y)
print("Cost at initial theta (zeros): ", cost)
print("Gradient at initial theta (zeros): \n", grad)
# 使用 scipy.optimize.fmin_cg 优化模型参数
args = (X, y)
maxiter = 200
# ====================== YOUR CODE HERE ======================
ret = op.fmin_cg(cost_function,
theta_initial-grad,
fprime=cost_gradient,
args=(X, y),
maxiter=200,
full_output=True)
theta_opt, cost_min, _, _, _ = ret
# ============================================================
theta_opt, cost_min, _, _, _ = ret
print("Cost at theta found by fmin_cg: ", cost_min)
print("theta: \n", theta_opt)
# 绘制分类面
plot_decision_boundary(theta_opt, X, y)
plt.show()
# 预测考试一得45分，考试二得85分的学生的录取概率
x_test = np.array([1, 45, 85.0])
prob = sigmoid(np.dot(theta_opt, x_test))
print("For a student with scores 45 and 85, we predict")
print("an admission probability of ", prob)
# 计算在训练集上的分类正确率
p = predict(theta_opt, X)
print("Train Accuracy: ", np.mean(p == y)*100)
def logistic_regression_reg(lmb=1.0):
"""针对第二组数据建立逻辑回归模型。"""
# 加载数据
data = np.loadtxt("data2.txt", delimiter=",")
X, y = data[:, :2], data[:, 2]
# 可视化数据
plot_data(X, y)
plt.legend()
plt.show()
# 计算具有正则项的代价与梯度
# 注意map_feature会自动加入一列 1
X = map_feature(X[:, 0], X[:, 1])
print("out0:",X.shape)
# 初始化参数
theta_initial = np.zeros_like(X[0, :])
# 计算并打印初始参数对应的代价与梯度
cost = cost_function_reg(theta_initial, X, y, lmb=lmb)
grad = cost_gradient_reg(theta_initial, X, y, lmb=lmb)
print("Cost at initial theta (zeros): ", cost)
print("Gradient at initial theta (zeros): \n", grad)
# 使用 scipy.optimize.fmin_cg 优化模型参数
args = (X, y, lmb)
maxiter = 200
# ====================== YOUR CODE HERE ======================
ret = op.fmin_cg(cost_function_reg,
theta_initial-grad,
fprime=cost_gradient_reg,
args=(X, y,lmb),
maxiter=400,
full_output=True)
theta_opt, cost_min, _, _, _ = ret
# ============================================================
theta_opt, cost_min, _, _, _ = ret
print("Cost at theta found by fmin_cg: ", cost_min)
print("theta: \n", theta_opt)
# 绘制分类面
plot_decision_boundary(theta_opt, X, y)
plt.title("lambda = " + str(lmb))
plt.show()
# 计算在训练集上的分类正确率
pred = predict(theta_opt, X)
print("Train Accuracy: ", np.mean(pred == y)*100)
if "__main__" == __name__:
# 分别完成无正则项和有正则项的逻辑回归问题
logistic_regression()
# 可选：尝试不同正则化系数lmb = 0.0, 1.0, 10.0, 100.0对分类面的影响
logistic_regression_reg(lmb=1.0)
此外，我之前想用线性回归那样的算法来实现逻辑回归（加了非线性以及交叉熵），但是由于逻辑回归的真实值在0,1之间变化，导致它不是凸函数，我计算了损失，发现损失总是在某个值和nan之间交替变化，最后发现在逻辑回归中使用了python 中的scipy模块中的optimizer非线性优化，代码中在op.fmin_cg（）这块。
线性回归是用的是线性优化。大家可以多查一些资料
如有错误，欢迎指出。
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