5-8.实现多元线性回归
作者：互联网
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
boston_data = datasets.load_boston()
X = boston_data.data
y = boston_data.target
X = X[y < 50.0]
y = y[y < 50.0]
以下自定义的类导入详情见5-5衡量回归算法的标准
from play_ML.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, seed = 666)
使用我们自己封装的简单线性回归法
使用pycharm在同级目录下新建工程play_ML
新建py脚本命名为LinearRegression
写入以下代码
import numpy as np
from .metrics import r2_score
class LinearRegression:
def __init__(self):
"""初始化Linear Regression模型"""
self.coef_ = None
self.interception_ = None
self._theta = None
def fit_normal(self, X_train, y_train):
"""根据训练数据X_train和y_train训练LinearRegression模型"""
assert X_train.shape[0] == y_train.shape[0], \
"the size of X_train must fit the size of y_train"
X_b = np.hstack([np.ones((len(X_train), 1)), X_train])
self._theta = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y_train)
self.interception_ = self._theta[0]
self.coef_ = self._theta[1:]
return self
def fit_gd(self, X_train, y_train, eta=0.01, n_iters=1e4):
"""根据训练数据集X_train和y_train使用梯度下降法训练LinearRegression模型"""
assert X_train.shape[0] == y_train.shape[0], \
"the size of X_train must be equal to the size of y_train"
def J(theta, X_b, y):
try:
return np.sum((y - X_b.dot(theta)) ** 2) / len(X_b)
except:
return float('inf')
"""偏导函数"""
def dJ(theta, X_b, y):
# res = np.empty(len(theta))
# res[0] = np.sum(X_b.dot(theta) - y)
# for i in range(1, len(theta)):
# res[i] = np.sum((X_b.dot(theta) - y).dot(X_b[:, i]))
# # 求和结果乘以某个样本的第i列
"""向量化的方式求解"""
return X_b.T.dot(X_b.dot(theta) - y) * 2 / len(y)
def gradient_descent(X_b, y, initial_theta, eta, n_iters=1e4, epsilon=1e-8):
theta = initial_theta
i_iters = 0
while i_iters < n_iters:
gradient = dJ(theta, X_b, y)
last_theta = theta
theta = theta - eta * gradient
if (abs(J(theta, X_b, y) - J(last_theta, X_b, y)) < epsilon):
break
i_iters += 1
return theta
X_b = np.hstack([np.ones((len(X_train), 1)), X_train])
initial_theta = np.zeros(X_b.shape[1])
eta = 0.01
self._theta = gradient_descent(X_b, y_train, initial_theta, eta)
self.interception_ = self._theta[0]
self.coef_ = self._theta[1:]
return self
def fit_sgd(self, X_train, y_train, n_iters=5, t0=5, t1=50):
"""根据训练数据集X_train和y_train使用随机梯度下降法训练LinearRegression模型"""
assert X_train.shape[0] == y_train.shape[0], \
"the size of X_train must be equal to the size of y_train"
assert n_iters >= 1, \
"所有样本至少遍历一次"
def dJ_sgd(theta, X_b_i, y_i):
return X_b_i.T.dot(X_b_i.dot(theta) - y_i) * 2.
def sgd(X_b, y, initial_theta, n_iters, t0=5, t1=50):
def learning_rate(t):
return t0 / (t + t1)
theta = initial_theta
m = len(X_b)
"""为了保证将所有的样本遍历到，所以采用嵌套循环，外循环是遍数，内循环是随机样本"""
for i_iters in range(n_iters):
shuffled_indexes = np.random.permutation(m)
X_b_new = X_b[shuffled_indexes]
y_new = y[shuffled_indexes]
for i in range(m):
"""直接从乱序样本中取值"""
gradient = dJ_sgd(theta, X_b_new[i], y_new[i])
"""学习率的计算也要做相应的改变"""
theta = theta - learning_rate(i_iters * m + i) * gradient
return theta
X_b = np.hstack([np.ones((len(X_train), 1)), X_train])
initial_theta = np.zeros(X_b.shape[1])
self._theta = sgd(X_b, y_train, initial_theta, n_iters, t0, t1)
self.interception_ = self._theta[0]
self.coef_ = self._theta[1:]
return self
def predict(self, X_predict):
assert self.interception_ is not None and self.coef_ is not None, \
"must be fitted before predicted"
assert X_predict.shape[1] == len(self.coef_), \
"the feature number of X_predict must be equal to the X_train"
X_b = np.hstack([np.ones((len(X_predict), 1)), X_predict])
return X_b.dot(self._theta)
def score(self, X_test, y_test):
"""根据测试数据集X_test和y_test判断当前模型的准确度"""
y_predict = self.predict(X_test)
return r2_score(y_test, y_predict)
def __repr__(self):
return "LinearRegression()"
导入自定义的回归算法
from play_ML.LinearRegression import LinearRegression
reg = LinearRegression()
reg.fit_normal(X_train, y_train)
LinearRegression()
reg.coef_
array([-1.12728076e-01, 3.83088307e-02, -4.09966537e-02, 7.27425361e-01,
-1.39378594e+01, 3.37684332e+00, -2.39762421e-02, -1.21315896e+00,
2.73164472e-01, -1.40027977e-02, -8.62432754e-01, 5.37440212e-03,
-3.59762900e-01])
reg.interception_
36.81014683461928
reg.score(X_test, y_test)
0.7989582352420577
标签：return,回归,多元,np,train,线性,theta,self,def 来源： https://www.cnblogs.com/ClarkGable/p/16095250.html