机器学习-线性回归实践

目标：使用Sklearn、numpy模块实现展现数据预处理、线性拟合、得到拟合模型，展现预测值与目标值，展现梯度下降；

一、导入模块

import numpy as np
np.set_printoptions(precision=2)
from sklearn.linear_model import LinearRegression, SGDRegressor
from sklearn.preprocessing import StandardScaler
from lab_utils_multi import  load_house_data
import matplotlib.pyplot as plt
from lab_utils_multi import  load_house_data, compute_cost, run_gradient_descent 
from lab_utils_multi import  norm_plot, plt_contour_multi, plt_equal_scale, plot_cost_i_w

dlblue = '#0096ff'; dlorange = '#FF9300'; dldarkred='#C00000';dlmagenta='#FF40FF'; dlpurple='#7030A0'; 
plt.style.use('./deeplearning.mplstyle')

二、导入数据集

x_train, y_train = load_house_data()
#设置特征变量
X_feature = ['size(sqft)','bedrooms','floors','age']

三、 训练数据集

scaler = StandardScaler()
X_norm = scaler.fit_transform(x_train)
print(f"Peak to Peak range by column in Raw        X:{np.ptp(x_train,axis=0)}")   
print(f"Peak to Peak range by column in Normalized X:{np.ptp(X_norm,axis=0)}")

四、创建模型并进行拟合

sgdr = SGDRegressor(max_iter=1000)
sgdr.fit(X_norm, y_train)
print(sgdr)
print(f"number of iterations completed: {sgdr.n_iter_}, number of weight updates: {sgdr.t_}")

五、 进行预测

b_norm = sgdr.intercept_
w_norm = sgdr.coef_

y_pred_sgd = sgdr.predict(X_norm)
y_pred = np.dot(X_norm, w_norm) + b_norm  

六、可视化预测值与目标值

fig,ax=plt.subplots(1,4,figsize=(12,3),sharey=True)
for i in range(len(ax)):
    ax[i].scatter(x_train[:,i],y_train, label = 'target')
    ax[i].set_xlabel(X_feature[i])
    ax[i].scatter(x_train[:,i],y_pred,color=dlorange, label = 'predict')
ax[0].set_ylabel("Price"); ax[0].legend();
fig.suptitle("target versus prediction using z-score normalized model")
plt.show()

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?七、梯度下降α=1e-7

_, _, hist = run_gradient_descent(x_train, y_train, 10, alpha = 1e-7)
plot_cost_i_w(x_train, y_train, hist)