Optional lab: Linear Regression using Scikit-LearnⅡ
scikit-learn是一个开源的、可用于商业的机器学习工具包，此工具包包含本课程中需要使用的许多算法的实现
Goals
In this lab you will utilize scikit-learn to implement linear regression using a close form solution based on the normal equation
Tools
You will utilize functions from scikit-learn as well as matplotlib and NumPy.
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
dlblue = '#0096ff'; dlorange = '#FF9300'; dldarkred='#C00000'; dlmagenta='#FF40FF'; dlpurple='#7030A0';
plt.style.use('./deeplearning.mplstyle')
Linear Regression, closed-form solution
Scikit-learn 有实现了closed-form 的线性回归模型 linear regression model
用之前lab中的数据
| Size (1000 sqft) | Price (1000s of dollars) |
|---|---|
| 1 | 300 |
| 2 | 500 |
Load the data set
X_train = np.array([1.0, 2.0]) #features
y_train = np.array([300, 500]) #target value
Create and fit the model
下面的代码使用scikit-learn执行回归
第一步是创建一个回归对象，第二步使用与对象关联的方法之一fit，这将执行回归，将参数与输入数据拟合，该工具包需要一个二维的X矩阵
linear_model = LinearRegression()
#X must be a 2-D Matrix
linear_model.fit(X_train.reshape(-1, 1), y_train)
输出如下
LinearRegression()
View parameters
参数 w \mathbf{w} w 和 b \mathbf{b} b 在scikit-learn中被称为系数和截距
b = linear_model.intercept_
w = linear_model.coef_
print(f"w = {w:}, b = {b:0.2f}")
print(f"'manual' prediction: f_wb = wx+b : {1200*w + b}")
输出如下
w = [200.], b = 100.00
'manual' prediction: f_wb = wx+b : [240100.]
Make predictions
调用预测函数predict生成预测
y_pred = linear_model.predict(X_train.reshape(-1, 1))
print("Prediction on training set:", y_pred)
X_test = np.array([[1200]])
print(f"Prediction for 1200 sqft house: ${linear_model.predict(X_test)[0]:0.2f}")
输出如下
Prediction on training set: [300. 500.]
Prediction for 1200 sqft house: $240100.00
Second Example
第二个例子来自早期的一个具有多特征的lab，最终的参数值和预测值与该lab未归一化的“长期运行”结果非常接近
未归一化的数据需要运行数小时才能产生结果，而下面的运行几乎是瞬间的，the closed-form solution 在较小数据集上运行良好，但在较大的数据集上可能对计算的要求很高
The closed-form solution 不需要归一化
# load the dataset
X_train, y_train = load_house_data()
X_features = ['size(sqft)','bedrooms','floors','age']
linear_model = LinearRegression()
linear_model.fit(X_train, y_train)
b = linear_model.intercept_
w = linear_model.coef_
print(f"w = {w:}, b = {b:0.2f}")
输出如下
w = [ 0.27 -32.62 -67.25 -1.47], b = 220.42
print(f"Prediction on training set:\n {linear_model.predict(X_train)[:4]}" )
print(f"prediction using w,b:\n {(X_train @ w + b)[:4]}")
print(f"Target values \n {y_train[:4]}")
x_house = np.array([1200, 3,1, 40]).reshape(-1,4)
x_house_predict = linear_model.predict(x_house)[0]
print(f" predicted price of a house with 1200 sqft, 3 bedrooms, 1 floor, 40 years old = ${x_house_predict*1000:0.2f}")
输出如下
print(f"Prediction on training set:\n {linear_model.predict(X_train)[:4]}" )
print(f"prediction using w,b:\n {(X_train @ w + b)[:4]}")
print(f"Target values \n {y_train[:4]}")
x_house = np.array([1200, 3,1, 40]).reshape(-1,4)
x_house_predict = linear_model.predict(x_house)[0]
print(f" predicted price of a house with 1200 sqft, 3 bedrooms, 1 floor, 40 years old = ${x_house_predict*1000:0.2f}")
Congratulations!
In this lab you:
- 使用了一个开源的机器学习工具包scikit-learn
- 使用该工具包中的 close-form solution 实现了线性回归