机器学习 线性模型里面的线性回归
哔哩哔哩视频地址 https://www.bilibili.com/video/BV1s54y1U7sG
线性模型 Python 实现
import numpy as np
from sklearn import linear_model
class LinearRegression:
def __init__(self):
self.w = None # 要训练的参数
self.n_features = None # 特征的个数
def fit(self,X,y): # 计算权重 W
"""
w=(X^TX)^{-1}X^Ty
"""
assert isinstance(X,np.ndarray) and isinstance(y,np.ndarray)
assert X.ndim==2 and y.ndim==1 # assert 断言,就是说后面的条件成立时执行下面代码,不满足时返回错误
assert y.shape[0]==X.shape[0]
n_samples = X.shape[0] #样本数量
self.n_features = X.shape[1] #特征个数,X.shape是个元组,元组的第二位代表列,也就是特征个数
extra = np.ones((n_samples,))
X = np.c_[X,extra] #是在行方向扩展连接两个矩阵,就是把两矩阵左右相加,要求行数相等,相当于 hstack https://blog.csdn.net/qq_43657442/article/details/108030183
if self.n_features < n_samples:
self.w = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y) # 其实就是X的广义逆乘Y,得到权重,详解见https://blog.csdn.net/qq_43657442/article/details/108032355
else:
raise ValueError('dont have enough samples')
def predict(self, X):
n_samples=X.shape[0]
extra = np.ones((n_samples,)) #产生一个二维数组,用这样的方式代表这个数组可行向量可列向量
X = np.c_[X, extra]
if self.w is None:
raise RuntimeError('cant predict before fit')
y_=X.dot(self.w)
return y_
if __name__ == '__main__':
X = np.array([[1.0,0.5,0.5],[1.0,1.0,0.3],[-0.1,1.2,0.5],[1.5,2.4,3.2],[1.3,0.2,1.4]])
y = np.array([1,0.5,1.5,2,-0.3])
lr = LinearRegression()
lr.fit(X,y)
X_test = np.array([[1.3,1,3.2],[-1.2,1.2,0.8]])
y_pre = lr.predict(X_test)
print(y_pre)
sklearn_lr = linear_model.LinearRegression()
sklearn_lr.fit(X,y)
sklearn_y_pre = sklearn_lr.predict(X_test)
print(sklearn_y_pre)
ridge_reg = linear_model.Ridge(alpha=0.05, solver='lsqr') # 岭回归,具有L2正则化的线性最小二乘法回归模型,损失函数是线性最小二乘函数,而正则化由l2-范数给出, alpha 是正则化的罚系数
ridge_reg.fit(X, y)
ridge_y_pre=ridge_reg.predict(X_test)
print(ridge_y_pre)
[video(video-9123WZkn-1597569613988)(type-bilibili)(url-https://player.bilibili.com/player.html?aid=839304367)(image-https://ss.csdn.net/p?http://i1.hdslb.com/bfs/archive/128f18852b354b62bdef00e9fe224b78ef283b41.jpg)(title-机器学习 线性模型里面的线性回归)]