ML之LoR：LoR之二分类之线性决策算法实现根据两课成绩分数~预测期末通过率(合格还是不合格)

ML之LoR：LoR之二分类之线性决策算法实现根据两课成绩分数~预测期末通过率(合格还是不合格)

目录

输出结果

代码设计

输出结果

LoR之二分类算法实现预测期末考试成绩合格还是不合格

LoR回归函数

代码设计

import pandas as pd
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
 
from scipy.optimize import minimize
 
from sklearn.preprocessing import PolynomialFeatures
 
pd.set_option('display.notebook_repr_html', False)
pd.set_option('display.max_columns', None)
pd.set_option('display.max_rows', 150)
pd.set_option('display.max_seq_items', None)
 
 
import seaborn as sns
sns.set_context('notebook')
sns.set_style('white')
 
def loaddata(file, delimeter):
    data = np.loadtxt(file, delimiter=delimeter)
    print('Dimensions: ',data.shape)
    print(data[1:6,:])
    return(data)
 
def plotData(data, label_x, label_y, label_pos, label_neg, axes=None):
     获得正负样本的下标(即哪些是正样本，哪些是负样本)
    neg = data[:,2] == 0
    pos = data[:,2] == 1
    
    if axes == None:
        axes = plt.gca()
    axes.scatter(data[pos][:,0], data[pos][:,1], marker='^', c='b', s=60, linewidth=2, label=label_pos)
    axes.scatter(data[neg][:,0], data[neg][:,1], c='y', s=60, label=label_neg)
    axes.set_xlabel(label_x)
    axes.set_ylabel(label_y)
    axes.legend(frameon= True, fancybox = True);
 
data = loaddata('data1.txt', ',')
X = np.c_[np.ones((data.shape[0],1)), data[:,0:2]]
y = np.c_[data[:,2]]
plotData(data, 'Exam 1 score', 'Exam 2 score', 'Pass', 'Fail')  绘图
 
 
 
 
定义sigmoid函数
def sigmoid(z):
    return(1 / (1 + np.exp(-z)))
 
定义损失函数
def costFunction(theta, X, y):
    m = y.size
    h = sigmoid(X.dot(theta))
    
    J = -1*(1/m)*(np.log(h).T.dot(y)+np.log(1-h).T.dot(1-y))
               
    if np.isnan(J[0]):
        return(np.inf)
    return(J[0])
 
求解梯度
def gradient(theta, X, y):
    m = y.size
    h = sigmoid(X.dot(theta.reshape(-1,1)))
    
    grad =(1/m)*X.T.dot(h-y)
 
    return(grad.flatten())
 
initial_theta = np.zeros(X.shape[1])
cost = costFunction(initial_theta, X, y)
grad = gradient(initial_theta, X, y)
print('Cost: \n', cost)
print('Grad: \n', grad)
 
最小化损失函数(梯度下降)，直接调用scipy里面的最小化损失函数的minimize函数
res = minimize(costFunction, initial_theta, args=(X,y), method=None, jac=gradient, options={'maxiter':400})
 
进行预测
def predict(theta, X, threshold=0.5):
    p = sigmoid(X.dot(theta.T)) >= threshold
    return(p.astype('int'))
 
 第一门课45分，第二门课85分的同学，拿到通过考试的概率
sigmoid(np.array([1, 45, 85]).dot(res.x.T))
p = predict(res.x, X) 
print('Train accuracy {}%'.format(100*sum(p == y.ravel())/p.size))
 
绘制二分类决策边界
plt.scatter(45, 85, s=60, c='r', marker='v', label='(45, 85)')
plotData(data, 'Exam 1 score', 'Exam 2 score', 'Pass', 'Failed')
x1_min, x1_max = X[:,1].min(), X[:,1].max(),
x2_min, x2_max = X[:,2].min(), X[:,2].max(),
xx1, xx2 = np.meshgrid(np.linspace(x1_min, x1_max), np.linspace(x2_min, x2_max))
h = sigmoid(np.c_[np.ones((xx1.ravel().shape[0],1)), xx1.ravel(), xx2.ravel()].dot(res.x))
h = h.reshape(xx1.shape)
plt.contour(xx1, xx2, h, [0.5], linewidths=1, colors='b');